Algebra 2 - Unit 2 Polynomial Operation Review P3

Polynomial Operation Review

By Henry Phan

Q1: ​Inline Dropdown - subtract polynomial

​Fill in the blank in the difference.

​ (7 + 2k² + 5k⁴ - 4k³) - (2k⁴ - 9k³ - 4k + 5k²)= ____ 5k³ - 3k² + 4k + 7

4k​

3k⁴​

2k​⁴

5k​²

Multiple Choice

(2n⁴ + 4n - 1 - 6n²) - (4n² - 2n³+ 5n⁴) = ____ + 2n³ - 10n² + 4n - 1

• -3n⁴

• 3n⁴

• 6n⁴

• -2n²

​Q2: Simplify the expression - add polynomial

​Simplify the expression: 6m + 7 - 5m³) + (2m +7m³ + 3)

​A. -2m³ + 6m - 10

​B. -2m³ + 8m - 10

​C. 2m³ + 8m + 10

​D. 2m³ + 6m - 8

​Q2: Simplify the expression - add polynomial

​Simplify the expression: 6m + 7 - 5m³) + (2m +7m³ + 3)

​A. -2m³ + 6m - 10

​B. -2m³ + 8m - 10

​C. 2m³ + 8m + 10

​D. 2m³ + 6m - 8

6m + 7 - 5m³ + 2m +7m³ + 3

​Q2: Simplify the expression - add polynomial

​Simplify the expression: 6m + 7 - 5m³) + (2m +7m³ + 3)

​A. -2m³ + 6m - 10

​B. -2m³ + 8m - 10

​C. 2m³ + 8m + 10

​D. 2m³ + 6m - 8

6m + 7 - 5m³ + 2m +7m³ + 3

√

Multiple Choice

(5a + 6 + 7a⁴) + (3a - 3a⁴ - 9)

• 10a⁴ - 8a + 3

• 4a⁴ + 8a - 3

• 6a⁴ + 4a + 15

• -4a +

Q3: Math Equation Respond​ - subtract polynomial

​Simplify: (5w + 3) - ( 7w + 3)

​

Q3: Math Equation Respond​ - subtract polynomial

​Simplify: (5w + 3) - ( 7w + 3)

​

​Distributive the second polynomial: 5w + 3 - 7w - 3

Q3: Math Equation Respond​ - subtract polynomial

​Simplify: (5w + 3) - ( 7w + 3)

-2​w

Fill in the Blank

Simplify (8t + 6) - (3t + 6)

Q4:​Multiple choice - multiply polynomial

​Which expression is equivalent to

(u -3)(5u³ + 2u² + 3u)²​

Q4:​Multiple choice - multiply polynomial

​Which expression is equivalent to

(u -3)(5u³ + 2u² + 3u)²​

​= u*5u³ + u*2u² + u*3u - 3*5u³ - 3*2u² - 3*3u

Q4:​Multiple choice - multiply polynomial

​Which expression is equivalent to

(u -3)(5u³ + 2u² + 3u)²​

​= u*5u³ + u*2u² + u*3u - 3*5u³ - 3*2u² - 3*3u

= 5u⁴ + 2u³ + 3u² - 15u³ - 6u² - 9u​

Q4:​Multiple choice - multiply polynomial

​Which expression is equivalent to

(u -3)(5u³ + 2u² + 3u)²​

​= u*5u³ + u*2u² + u*3u - 3*5u³ - 3*2u² - 3*3u

= 5u⁴ + 2u³ + 3u² - 15u³ - 6u² - 9u​

​= 5u⁴ - 13u³ - 3u² - 9u

Multiple Choice

Find the product

$$\left(2k\ -\ 5\right)\left(7k^2\ -5k\ +4\right)$$  

• $$14k^3\ -45k^2\ +\ 33k\ -20$$  

• $$14k^3\ +\ 45k^2-33k\ +20$$  

• $$14k^3-45k^2-33k\ +\ 20$$  

• $$14k^3\ +\ 33k^2\ -45k\ -20$$  

​Q5: Multiple Choice

​(w⁴ - 3w³ + 4w² + 7) - (w⁴ - 4w³ + 2w² + 7w + 1)

​by distributing the negative sign to each term in the second polynomial as following:

​Q5: Multiple Choice

​(w⁴ - 3w³ + 4w² + 7) - (w⁴ - 4w³ + 2w² + 7w + 1)

​by distributing the negative sign to each term in the second polynomial as following:

​w⁴ - 3w³ + 4w² + 7 - w⁴ + 4w³ - 2w² - 7w - 1

​Q5: Multiple Choice

​(w⁴ - 3w³ + 4w² + 7) - (w⁴ - 4w³ + 2w² + 7w + 1)

​by distributing the negative sign to each term in the second polynomial as following:

​w⁴ - 3w³ + 4w² + 7 - w⁴ + 4w³ - 2w² - 7w - 1

​w⁴ - 3w³ + 4w² + 7 - w⁴ + 4w³ - 2w² - 7w - 1

​Q5: Multiple Choice

​(w⁴ - 3w³ + 4w² + 7) - (w⁴ - 4w³ + 2w² + 7w + 1)

​by distributing the negative sign to each term in the second polynomial as following:

​w⁴ - 3w³ + 4w² + 7 - w⁴ + 4w³ - 2w² - 7w - 1

​w⁴ - 3w³ + 4w² + 7 - w⁴ + 4w³ - 2w² - 7w - 1

​w³ + 2w² - 7w + 6

Multiple Choice

Simplify: (4c³ + 6c² + 7) - (4c³ - 3c² + 9c - 5)

• -9c² - 9c - 2

• -9c² - 9c - 12

• 9c² - 9c + 12

• 9c² + 9c + 2

​Q6: Multiple Choice - multiply polynomial

​Find the product: (3v - 4)(7v² - 4v + 5) =

​This is the result of systematically multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms

​Q6: Multiple Choice - multiply polynomial

​Find the product: (3v - 4)(7v³ - 4v² + 5v) =

​This is the result of systematically multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms

​21v⁴ - 12v³ + 15v² - 28v³ + 16v² - 20v​

​Q6: Multiple Choice - multiply polynomial

​Find the product: (3v - 4)(7v³ - 4v² + 5t) =

​This is the result of systematically multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms

​21v⁴ - 12v³ + 15v² - 28v³ + 16v² - 20v​

​21v⁴ - 40v³ + 31v² - 20v​

Multiple Choice

Find the product

(t - 3)(5t³ + 2t² + 3t)

• -5t⁴ + 13t³ - 3t² - 9t

• 5t⁴ + 13t³ + 3t² + 9t

• 5t⁴ - 13t³ - 3t² - 9t

• 5t³ - 13t² - 3t - 9

​Q7: Multiple Choice - add polynomial

​Simplify

(3a² - 5a + 8) + (7a² + 3a)​

​This result from correctly combining like terms:

​Q7: Multiple Choice - add polynomial

​Simplify

(3a² - 5a + 8) + (7a² + 3a)​

​This result from correctly combining like terms:

​3a² - 5a + 8 + 7a² + 3a

​Q7: Multiple Choice - add polynomial

​Simplify

(3a² - 5a + 8) + (7a² + 3a)​

​This result from correctly combining like terms:

​3a² - 5a + 8 + 7a² + 3a

​10a² - 2a + 8

Multiple Choice

(6w² - 5w + 3) + (2w² + 5w)

• 4w² - 10w + 3

  subtracting the second polynomial

• 8w² + 10w + 3

  ignoring the negative signs

• 8w² + 3.

  This result

  (6w² + 2w²)

  + (-5w + 5w) + 3

• w² + 7w

  combining the coefficents within each set of parentheses

​Q8: Multiple choice - Binomial Expansion

​Expand completely: (5v - 1)³

​Q8: Multiple choice - Binomial Expansion

​Expand completely: (5v - 1)³

​Coefficients:

1 3 3 1​

​Q8: Multiple choice - Binomial Expansion

​Expand completely: (5v - 1)³

(5v - 1)³ = (5v)³ - 3(5v)²(1) + 3(5V)(1)² - (1)³

​Q8: Multiple choice - Binomial Expansion

​Expand completely: (5v - 1)³

(5v - 1)³ = (5v)³ - 3(5v)²(1) + 3(5V)(1)² - (1)³

​(5v - 1)³ = 125v³ - 75v² + 15v - 1

Multiple Choice

Expand completely

(6k - 1)³

• 216k³ - 108k² + 6k - 1

• 216k³ - 108k² + 18k - 1

• 216k³ + 108k² - 18k + 1

• 36k³ - 18k² + 108k - 3

​Q9: Multiple Choice - Binomial Expansion

​Find the 3rd term in the expansion of (t + 3)³

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients:

1 3 3 1​

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients:

1 3 3 1​

​1(t)(3) 3(t)(3) 3(t)(3) 1​(t)(3)

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients: 1 3 3 1​

​1(t)³(3) 3(t)²(3) 3(t)¹(3) 1​(t)⁰(3)

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients: 1 3 3 1​

​1(t)³(3)⁰ 3(t)²(3)¹ 3(t)¹(3)² 1​(t)⁰(3)³

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients: 1 3 3 1​

​1(t)³(3)⁰ 3(t)²(3)¹ 3(t)¹(3)² 1​(t)⁰(3)³

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients: 1 3 3 1​

​1(t)³(3)⁰ 3(t)²(3)¹ 3(t)¹(3)² 1​(t)⁰(3)³

​(t)³ 3(t)²(3) 3(t)(3)² (3)³

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients: 1 3 3 1​

​(t)³ 3(t)²(3) 3(t)(3)² (3)³

​(t)³ + 3(t)²(3) + 3(t)(3)² + (3)³

​Q9: Multiple Choice

​Find the 3rd term in the expansion of (t + 3)³

​Coefficients: 1 3 3 1​

​(t)³ + 3(t)²(3) + 3(t)(3)² + (3)³

​t³ + 9t² + 27t + 27

Thus the 3rd term: 27t

Multiple Choice

Find the 3rd term in the expansion (u + 4)³

• 48u

• 12u²

• 64

• u³

​Q10: Multiple choice: Binomial Expansion

​Expand completely: (ma - na)⁴

​Q10: Multiple choice: Binomial Expansion

​Expand completely: (ma - na)⁴

​Coefficients (according to the pascal's triangles): 1 4 6 4 1

​Q10: Multiple choice: Binomial Expansion

​Expand completely: (ma - na)⁴

​Coefficients (according to the pascal's triangles): 1 4 6 4 1

​Operation: since it has a negative sign "-" then: coefficient now is: 1 -4 6 -4 +1

​Q10: Multiple choice: Binomial Expansion

​Expand completely: (ma - na)⁴

​Coefficients (according to the pascal's triangles): 1 4 6 4 1

​Operation: since it has a negative sign "-" then: coefficient now is: 1 -4 6 -4 +1

​term 1st (L-> R): (ma)⁴ (ma)³ (ma)² (ma) + ____

​term 2nd (L<-R): ___ (na) (na)² (na)³ (na)⁴

​Q10: Multiple choice: Binomial Expansion

​Expand completely: (ma - na)⁴

​Coefficients (according to the pascal's triangles): 1 4 6 4 1

​Operation: since it has a negative sign "-" then: coefficient now is: 1 -4 6 -4 +1

​term 1st (L-> R): (ma)⁴ (ma)³ (ma)² (ma) + ____

​term 2nd (L<-R): ___ (na) (na)² (na)³ (na)⁴

​Then(2 terms): (ma)⁴ -4(ma)³(na) +6(ma)²(na)² -4(ma)(na)³ +(na)⁴

​Q10: Multiple choice: Binomial Expansion

​Expand completely: (ma - na)⁴

​Coefficients (according to the pascal's triangles): 1 4 6 4 1

​Operation: since it has a negative sign "-" then: coefficient now is: 1 -4 6 -4 +1

​term 1st (L-> R): (ma)⁴ (ma)³ (ma)² (ma) + ____

​term 2nd (L<-R): ___ (na) (na)² (na)³ (na)⁴

​Then(2 terms): (ma)⁴ -4(ma)³(na) +6(ma)²(na)² -4(ma)(na)³ +(na)⁴

​Thus (simplify): m⁴a⁴ - 4m⁴a⁴n + 6m²a⁴n²- 4mn³a⁴ + n⁴a⁴

Multiple Choice

Expand (ak - bk)⁴

• (ak)⁴ + 4(ak)³(bk) + 6(ak)²(bk)² + 4(ak)(bk)³ + (bk)⁴

• (ak)⁴ - 4(ak)³(bk) + 6(ak)²(bk)² - 4(ak)(bk)³ + (bk)⁴

• (ak)⁴ + 4(ak)³(bk) - 6(ak)²(bk)² + 4(ak)(bk)³ + (bk)⁴

• (ak)⁴ - (ak)³(bk) + (ak)²(bk)² - (ak)(bk)³ + (bk)⁴

Q11: Multiple choice - inverse function

​Find h^-1(x). h(x) = 4x - 10

Q11: Multiple choice - inverse function

​Find h^-1(x). h(x) = 4x - 10

• Let y = h(x) then y = 4x - 10

• switch x <=> y: x = 4y - 10

​

Q11: Multiple choice - inverse function

​Find h^-1(x). h(x) = 4x - 10

• Let y = h(x) then y = 4x - 10

• switch x <=> y: x = 4y - 10

• solve for y: then ​

​

Q11: Multiple choice - inverse function

​Find h^-1(x). h(x) = 4x - 10

• Let y = h(x) then y = 4x - 10

• switch x <=> y: x = 4y - 10

• solve for y: then ​

​

​ x = 4y - 10

x + 10 = 4y​ (by adding 10 for 2 both sides

Q11: Multiple choice - inverse function

​Find h^-1(x). h(x) = 4x - 10

• Let y = h(x) then y = 4x - 10

• switch x <=> y: x = 4y - 10

• solve for y: then ​

​

​ x = 4y - 10

x + 10 = 4y​ (by adding 10 for 2 both sides)

​Thus: (x + 10)/4 = y​ (by dividing 4 for 2 sides)

Multiple Choice

Find k^-1(x). Let k(x) = 4x - 45

• $$\frac{x-4}{45}$$  

• $$\frac{45-x}{4}$$  

• $$\frac{x-45}{4}$$  

• $$\frac{x+45}{4}$$  

​Q12: Multiple choice - Inverse Function

​Find the inverse of the function: f(t) = - t + 7​

​Q12: Multiple choice - Inverse Function

​Find the inverse of the function: f(t) = - t + 7​

​Let y = - t + 7

​Q12: Multiple choice - Inverse Function

​Find the inverse of the function: f(t) = - t + 7​

​Let y = - t + 7

​Switch t <=> y then t = -y + 7

​Q12: Multiple choice - Inverse Function

​Find the inverse of the function: f(t) = - t + 7​

​Let y = - t + 7

​Switch t <=> y then t = -y + 7

​Solve for y then: t = - y + 7

t - 7 = -y​ by adding 7 for both sides

​Q12: Multiple choice - Inverse Function

​Find the inverse of the function: f(t) = - t + 7​

​Let y = - t + 7

​Switch t <=> y then t = -y + 7

​Solve for y then: t = - y + 7

t - 7 = -y​ by adding 7 for both sides

​Because y is negative, we dividing -1 for 2 sides

​Then -t + 7 = y

Multiple Choice

Find the inverse of the function:

g(y) = - y + 9

• g^-1(y) = -y + 9

• g^-1(y) = y + 9

• g^-1(y) = y - 9

• g^-1(y) = 9y

​Q13: Multiple choice - combination - multiply

​Let k(x) = x² + 4x - 7

Let l(x) = 4x + 5​

What is (k⋅l)x?

​Q13: Multiple choice - combination - multiply

​Let k(x) = x² + 4x - 7

Let l(x) = 4x + 5​

What is (k⋅l)x?

​(k⋅l)x = (x² + 4x - 7)(4x + 5)

​Q13: Multiple choice - combination - multiply

​Let k(x) = x² + 4x - 7

Let l(x) = 4x + 5​

What is (k⋅l)x?

​(k⋅l)x = (x² + 4x - 7)(4x + 5)

​(k⋅l)x = (x²)(4x) + (4x)(4x) - (7)(4x) + (x²)(5) + (4x)(5) - (7)(5)

​Q13: Multiple choice - combination - multiply

​Let k(x) = x² + 4x - 7

Let l(x) = 4x + 5​

What is (k⋅l)x?

​(k⋅l)x = (x² + 4x - 7)(4x + 5)

​(k⋅l)x = (x²)(4x) + (4x)(4x) - (7)(4x) + (x²)(5) + (4x)(5) - (7)(5)

​(k⋅l)x = 4x³ + 16x² - 28x + 5x² + 20x - 35

​Q13: Multiple choice - combination - multiply

​Let k(x) = x² + 4x - 7

Let l(x) = 4x + 5​

What is (k⋅l)x?

​(k⋅l)x = (x² + 4x - 7)(4x + 5)

​(k⋅l)x = (x²)(4x) + (4x)(4x) - (7)(4x) + (x²)(5) + (4x)(5) - (7)(5)

​(k⋅l)x = 4x³ + 16x² - 28x + 5x² + 20x - 35 = 4x³ + 21x² - 8x - 35

Multiple Choice

h(x) = x² + 4x - 9

j(x) = 3x + 7

What is $$\left(h\cdot j\right)x$$  ?

• 3x³ + 19x² + x - 63

  $$\left(h\cdot j\right)x\ =$$  

  (x² + 4x - 9)(3x + 7)

  = 3x³ + 19x² + x - 63

• 3x³ + 19x² +12 x + 63

  This is result of not distributing the negative sign when multiplying 3x + 7 by -9

• x³ + 19x² + x - 63

  This is the result of not understanding that when multiplying two x together

• x³ + 19x² + x - 63

  This is the result of not understanding that when multiplying two x together.

​Q14: Multiple choice - combination: subtract and evaluate

​k(t) = 3t + 7

l(t) = 3t + 4​

Find (k - l)(-4)​

​Q14: Multiple choice - combination: subtract and evaluate

​k(t) = 3t + 7

l(t) = 3t + 4​

Find (k - l)(-4)​

​(k - l)t = (3t + 7) - (3t + 4)

​Q14: Multiple choice - combination: subtract and evaluate

​k(t) = 3t + 7

l(t) = 3t + 4​

Find (k - l)(-4)​

​(k - l)t = (3t + 7) - (3t + 4)

​= 3t + 7 - 3t - 4

​Q14: Multiple choice - combination: subtract and evaluate

​k(t) = 3t + 7

l(t) = 3t + 4​

Find (k - l)(-4)​

​(k - l)t = (3t + 7) - (3t + 4)

​= 3t + 7 - 3t - 4

​= 3

Multiple Choice

let f(t) = 5t + 9

g(t) = 5t + 7

Find $$\left(f-g\right)$$  (-2)

• 16

• 2

• -2

• -16

​Q15: Multiply choice - Combination and Evaluate

​Given that f(t) = t - 9 and g(t) = t - 3

Find (f + g) (2)​

​Q15: Multiply choice - Combination and Evaluate

​Given that f(t) = t - 9 and g(t) = t - 3

Find (f + g) (2)​

​(f + g)t = t - 9 + t - 3 = 2t - 12

​Q15: Multiply choice - Combination and Evaluate

​Given that f(t) = t - 9 and g(t) = t - 3

Find (f + g) (2)​

​(f + g)t = t - 9 + t - 3 = 2t - 12

​Then (f + g) (2) = 2(2) - 12 = -8

Multiple Choice

Given f(t) = t - 4 and g(t) = t - 6, find [f + g) (3)

• 6

• -10

• -4

• 4

​Q16: Multiple choice - Composite Function

​if g(t) = 3t - 3 and f(t) = 3t - 5. Find g(f(3)

​Q16: Multiple choice - Composite Function

​if g(t) = 3t - 3 and f(t) = 3t - 5. Find g(f(3)

​g(f(x)) = 3 [ f(x) ] - 3 = 3 [3t - 5] - 3

​Q16: Multiple choice - Composite Function

​if g(t) = 3t - 3 and f(t) = 3t - 5. Find g(f(3)

​g(f(x)) = 3 [ f(x) ] - 3 = 3 [3t - 5] - 3

​g(f(3)) = 3 [ 3×3 - 5] = 12

Multiple Choice

If g(t) = 4t - 4 and f(t) = 4t - 5, find $$g\left(f\left(2\right)\right)$$  

• 3

• -8

• 8

• 12

​Q17: Multiple Choice - Combination - dividing

​Q(x) = x - 9

R(x) ​= -3x² - x

Find (Q/R)(x)​

​Q17: Multiple Choice - Combination - dividing

​Q(x) = x - 9

R(x) ​= -3x² - x

Find (Q/R)(x)​

​(Q/R)x = (x - 9) ÷ (-3x² - x)

Multiple Choice

Let f(a) = a - 1

g(a) = -2a² - a

Find $$\left(\frac{f}{g}\right)\left(a\right)$$  

• $$\frac{-2a^2-a}{a-1}$$  

• $$\frac{a-1}{-2a^2-a}$$  

• $$\frac{-2a^3-a}{a\ -\ 1}$$  

• $$\frac{2}{a-1}$$  

​Q18: Multiple choice - Combination - multiply

​f(n) = n³ + 4n² and g(n) = 5n + 2, then (f⋅g)(n)

​Q18: Multiple choice - Combination - multiply

​f(n) = n³ + 4n² and g(n) = 5n + 2, then (f⋅g)(n)

​(f⋅g)n = (n³ + 4n²)(5n + 2)

​Q18: Multiple choice - Combination - multiply

​f(n) = n³ + 4n² and g(n) = 5n + 2, then (f⋅g)(n)

​(f⋅g)n = (n³ + 4n²)(5n + 2)

​(f⋅g)n = (n³)(5n + 2) + (4n)(5n + 2)

​Q18: Multiple choice - Combination - multiply

​f(n) = n³ + 4n² and g(n) = 5n + 2, then (f⋅g)(n)

​(f⋅g)n = (n³ + 4n²)(5n + 2)

​(f⋅g)n = (n³)(5n + 2) + (4n)(5n + 2)

​(f⋅g)n = 5n⁴+ 2n³ + 20n² + 8n

​Q18: Multiple choice - Combination - multiply

​f(n) = n³ + 4n² and g(n) = 5n + 2, then (f⋅g)(n)

​(f⋅g)n = (n³ + 4n²)(5n + 2)

​(f⋅g)n = (n³)(5n + 2) + (4n²)(5n + 2)

​(f⋅g)n = 5n⁴+ 2n³ + 20n³ + 8n²

​Q18: Multiple choice - Combination - multiply

​f(n) = n³ + 4n² and g(n) = 5n + 2, then (f⋅g)(n)

​(f⋅g)n = (n³ + 4n²)(5n + 2)

​(f⋅g)n = (n³)(5n + 2) + (4n²)(5n + 2)

​(f⋅g)n = 5n⁴+ 2n³ + 20n³ + 8n²

​(f⋅g)n = 5n⁴+ 22n³ + 8n²

Multiple Choice

f(n) = n² + 6n and g(n) = 7n² + 4n, then find $$\left(f\cdot g\right)n$$  

• 7n⁴ - 46n³ - 24n²

• 7n⁴ + 46n³ + 24n²

• -7n⁴ + 46n³ - 24n²

• -7n⁴ - 46n³ + 24n²

​Q19: Multiple choice - combination - subtract

​Two function are given. Find (g - h)(x)

g(x) = 5x - 3

h(x) = ​4x - 7

​Q19: Multiple choice - combination - subtract

​Two function are given. Find (g - h)(x)

g(x) = 5x - 3

h(x) = ​4x - 7

​(g - h)x = (5x - 3) - (4x - 7)

​Q19: Multiple choice - combination - subtract

​Two function are given. Find (g - h)(x)

g(x) = 5x - 3

h(x) = ​4x - 7

​(g - h)x = (5x - 3) - (4x - 7)

​(g - h)x = 5x - 3 - 4x + 7

​Q19: Multiple choice - combination - subtract

​Two function are given. Find (g - h)(x)

g(x) = 5x - 3

h(x) = ​4x - 7

​(g - h)x = (5x - 3) - (4x - 7)

​(g - h)x = 5x - 3 - 4x + 7

​= x + 4

Multiple Choice

Two functions are given. Find (g - h)x

g(x) = 6x - 7 and h(x) = 5x - 9

• 11x + 2

• 11x - 16

• x + 2

• x - 2

​Q20: Multiple choice - combination - divide

​Given g(n) = 4n + 5 and f(n) = 3n, find (g/f) (n)

​Q20: Multiple choice - combination - divide

​Given g(n) = 4n + 5 and f(n) = 3n, find (g/f) (n)

​(g/f)n = (4n + 5) ∕ (3n)

Multiple Choice

Given g(n) = 6n + 7 and f(n) = 5n, find $$\left(\frac{g}{f}\right)\left(n\right)$$  

• $$\frac{7}{6n\ +\ 5n}$$  

• $$\frac{5n\ +\ 7}{6n}$$  

• $$\frac{5n}{6n\ +\ 7}$$  

• $$\frac{6n\ +7}{5n}$$  

​Q21: Multiple Choice - composition

​If f(t) = t + 5 and g(t) = t³ - 3t, find (f ₒ g)(t)

​Q21: Multiple Choice - composition

​If f(t) = t + 5 and g(t) = t³ - 3t, find (f ₒ g)(t)

​(f ₒ g)t = f(g(t)) =

​Q21: Multiple Choice - composition

​If f(t) = t + 5 and g(t) = t³ - 3t, find (f ₒ g)(t)

​(f ₒ g)t = f(g(t)) = [ g(t) ] + 5

​Q21: Multiple Choice - composition

​If f(t) = t + 5 and g(t) = t³ - 3t, find (f ₒ g)(t)

​(f ₒ g)t = f(g(t)) = [ g(t) ] + 5

​= [t³ - 3t] + 5

​Q21: Multiple Choice - composition

​If f(t) = t + 5 and g(t) = t³ - 3t, find (f ₒ g)(t)

​(f ₒ g)t = f(g(t)) = [ g(t) ] + 5

​= [t³ - 3t] + 5

​= t³ - 3t + 5

Multiple Choice

If f(t) = t + 7, g(t) = t³ - 2t, find $$\left(f\degree g\right)\left(t\right)$$  

• (t + 7)³ - 2(t + 7)

• t³ - 2t + 7

• -t³ + 2t - 7

• t³ + 21t² + 147t + 357

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​(f ₒ g)(x) = f(g(x))

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​(f ₒ g)(x) = f(g(x))

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​(f ₒ g)(x) = f(g(x))

​(f ₒ g)(x) = f(g(x)) = 5 [ g(x) ] + 6

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​(f ₒ g)(x) = f(g(x))

​(f ₒ g)(x) = f(g(x)) = 5 [ g(x) ] + 6

​(f ₒ g)(x) = f(g(x)) = 5 [6x + 7] + 6

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​(f ₒ g)(x) = f(g(x))

​(f ₒ g)(x) = f(g(x)) = 5 [ g(x) ] + 6

​(f ₒ g)(x) = f(g(x)) = 5 [6x + 7] + 6

​(f ₒ g)(x) = f(g(x)) = 30x + 35 + 6

​Q22:Multiple choice - Composition

​f(x) = 5x + 6

g(x) = 6x + 7

Find (f ₒ g) (x)​

​(f ₒ g)(x) = f(g(x))

​(f ₒ g)(x) = f(g(x)) = 5 [ g(x) ] + 6

​(f ₒ g)(x) = f(g(x)) = 5 [6x + 7] + 6

​(f ₒ g)(x) = f(g(x)) = 30x + 35 + 6 = 30x + 41

Multiple Choice

f(x) = 8x + 5

g(x) = 7x + 3

Find $$\left(f\degree g\right)\left(x\right)$$  

• 56x + 29

• 56x + 38

• 56x² + 24x + 5

• 56x² + 35x + 3