Linear Functions & Slope-Intercept Form

FUNCTION OPERATIONS
INTRODUCTION

​Dr. Tom Giles

What you'll learn today:

• Review of functions.

• Perform operations on functions, including Addition, Subtraction, Multiplication, & Division.

Multiple Choice

Given f(x) = x - 5, find f(a+1).

• (a + 1) - 5

• a + 1 - 5

• a - 5

• a -4

Adding Functions

Multiple Choice

• $$3x^2-8x-2$$

• $$3x^2+8x+2$$

• $$3x^2+8x-2$$

• $$3x^2-8x+2$$

Multiple Choice

f(n)=2n+1 g(n)=3n Find f(n)+g(n)

• 5n+1

• -5n+1

• -2n+1

• -6n-1

Multiple Choice

f(n)=n²+4n g(n)=-n-5 Find f(n)+g(n)

• n²+3n-5

• -n³+2n-7

• n³+3n-3n

• n²-3n-5

Multiple Choice

f(n)=n²+4n g(n)=-n-5 Find f(n)+g(n)

• n²+3n-5

• -n³+2n-7

• n³+3n-3n

• n²-3n-5

Multiple Choice

f(x)= 4x-7

g(x)= 6x-8

Find f(x)+g(x)

• 2x+15

• 10x-15

• -2x-15

• 10x+1

Subtracting Functions

Multiple Choice

f(n)=x²+1 g(n)=2x-5 Find f(n)-g(n)

• x²-2x+6

• -x²+2x+4

• -x²-2x-6

• x²-2x-4

Multiple Choice

f(x) = x²+9 g(x) = x-9 Find f(x)-g(x). 

• x²+x+9

• x²-x+9

• x²-x

• x²-x+18

Multiple Choice

f(x)=x²+1 g(x)=2x-5 Find f(x)-g(x)

• x²-2x+6

• -x²+2x+4

• -x²-2x-6

• x²-2x-4

Multiple Choice

f(n)=x²+1 g(n)=2x-5 Find f(n)-g(n)

• x²-2x+6

• -x²+2x+4

• -x²-2x-6

• x²-2x-4

Multiplying Functions

Dividing Functions

Multiple Choice

$$f\left(x\right)=x^2-4x-32$$  

and  $$g\left(x\right)=x+4$$  . What is  $$\frac{f\left(x\right)}{g\left(x\right)}$$  ?

• x-12

• x+4

• x-8

• x-3

Open Ended

What is  $$\frac{f\left(x\right)}{g\left(x\right)}$$  ? $$f\left(x\right)=x^2-7x-30\ and\ g\left(x\right)=x+3$$  

Multiple Choice

$$f\left(x\right)=x^2-4x-32$$  

and  $$g\left(x\right)=x+4$$  . What is  $$\frac{f\left(x\right)}{g\left(x\right)}$$  ?

• x-12

• x+4

• x-8

• x-3

Multiple Choice

f(x) = 6x² + 3x + 2 and g(x) = x - 7

Find f(x) * g(x)

• 6x³ - 39x² - 19x + 14

• 6x³ - 39x² - 21x - 14

• 6x³ - 39x² - 19x - 14

• 6x³ - 45x² - 19x + 14

Multiple Choice

f(x) = 3 and g(x) = -2x + 5 Find f(x) * g(x)

• 6x + 15

• 6x - 15

• -6x + 15

• 6x - 8

Multiple Choice

f(x) = 4x + 1 and g(x) = 4x - 3 Find f(x) * g(x)

• 16x² + 8x - 3

• 16x² - 8x + 3

• 16x² - 8x - 3

• 16x² - 16x - 3

Multiple Choice

Given f(x) = 3x² + 1, what is f(t + 2)?

• 3t² + 3

• (3t + 2)² + 1

• 3(t + 2)² + 1

• none of these

Multiple Choice

Given

f(x) = 3x² + 7x         g(x) = 2x² - x - 1       find (f + g)(x).

• 11x² - 1

• 5x⁴ + 6x² - 1

• 5x² + 6x - 1

• 5x² + 8x - 1

Multiple Choice

f(x) = x²+9

g(x) = x-9

Find f(x)-g(x).

• x²+x+9

• x²-x+9

• x²-x

• x²-x+18

Multiple Choice

$$If\ f\left(x\right)\ =\ 2x^2-5x\ and\ g\left(x\right)\ =3x^2$$  

Find f(2).

• -2

• -18

• 24

• 6

Multiple Choice

f(x) = 4x+8

g(x) = x+3,

Find f(x) * g(x)

• 4x²+24

• 4x²+20x+24

• 4x²+12x+24

• 4x²+4x+24

Poll

Consider this function. What is the middle term? What is "b"?  $$x^2-9$$  

• 0

• 1

• -9

Multiple Choice

So what are the factors of $$x^2-9$$  ?

• (x-1)(x+9)

• (x-3)(x+3)

• (x-9)(x+1)