Free Printable 1st semester Alg 2

1.

The inverse of the function f(x) is written as ...

a)

f ^-1(x)

b)

f ²(x)

c)

f '(x)

d)

f ⁺(x)

2.

The inverse has been reflected over which line?

a)

y = x

b)

x = 0

c)

y = 0

d)

x = -y

3.

Which graph represents the functions f(x) and f^-1(x)?

a)

b)

c)

d)

4.

What is the inverse of the points (1,3)(2,4)(6,2)?

a)

(2,6)(3,1)(4,2)

b)

(-3,-1)(-4,-2)(-2,-6)

c)

(1,3)(2,4)(6,2)

d)

(-1,-3)(-2,-4)(-6,-2)

5.

Determine which type of function the following is:

$y=5x^2-7x+9$

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

6.

Determine which type of function the following is:

$y=5\left(6.1\right)^x-12$

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

7.

Determine which type of function the following is:

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

8.

Determine what type of function the following table is:

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

9.

Determine what type of function the following table is:

a)

Linear

b)

Quadratic

c)

Exponential

d)

Not a function

10.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

11.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

12.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

13.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

14.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

15.

Write

7^{\frac{1}{2}}

in radical form.

a)

$7^2$

b)

$\sqrt{7}$

c)

16.

Write

6^{\frac{3}{2}}

in radical form.

a)

b)

c)

d)

17.

Write

\left(\sqrt{10}\right)^3

in exponential form.

a)

$10^{\frac{1}{3}}$

b)

$10^{\frac{2}{3}}$

c)

$10^{\frac{3}{2}}$

d)

$10^{\frac{1}{2}}$

18.

Write the expression above in exponential form.

a)

$2^{\frac{4}{5}}$

b)

$2^{\frac{5}{4}}$

c)

$2^{\frac{1}{5}}$

d)

$4^{\frac{5}{2}}$

19.

What is the parent function of square root functions?

a)

f(x) = x

b)

f(x) = √x

c)

f(x) = -√x

d)

f(x) = x²

20.

What are the transformations of this functions compared to the parent function?

a)

Shifted down 2

b)

Shifted up 2

c)

Shifted left 2

d)

Shifted right 2

21.

Which of these equations shifts a radical equation right 5 units and down one unit?

a)

$y=\sqrt{x-5}-1$

b)

$y=\sqrt{x+5}-1$

c)

$y=\sqrt{x-5}+1$

d)

$y=\sqrt{x+5}+1$

22.

Determine the equation for the graph.

a)

$y=2\sqrt{x}-4$

b)

$y=-\sqrt{x-4}$

c)

$y=2\sqrt{x}$

d)

$y=2\sqrt{x}+4$

23.

Change 6.75% to a decimal.

a)

67.5

b)

.675

c)

675

d)

.0675

24.

Semi-Annually means how many times a year?

a)

4

b)

2

c)

1

d)

6

25.

Monthly means how many times a year?

a)

4

b)

12

c)

52

d)

365

26.

Bruno was given $2000 when he turned 3 years old. His parents invested it at a 2% interest rate compounded annually. No deposits or withdrawls were made. Which expression can be used to determine how much money Bruno had in the account when he turned 16?

a)

2000(1+0.02)¹³

b)

2000(1-0.02)¹³

c)

2000(1+0.02)¹⁶

d)

2000(1-0.02)¹⁶

27.

What does the n stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

28.

What does the r stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

29.

What does the P stand for in this formula?

a)

Initial amount

b)

Final amount

c)

Rate

d)

Time

e)

The number of times compounded per year

30.

Write the exponential equation as a logarithm
6³=216

a)

log₆(3) = 216

b)

log₃(6) = 216

c)

log₆(216)=3

d)

log₂₁₆(6)=3

31.

Rewrite 3⁴ = 81 in logarithmic form.

a)

log₃4 = 81

b)

log₈₁3 = 4

c)

log₃81 = 4

d)

log₄81 = 3

32.

Change to Exponential Form:
log₆36 = 2

a)

2⁶=36

b)

6²=36

c)

36²=6

d)

36⁶=2

33.

Rewrite log_pt = m in exponential form.

a)

p^t = m

b)

t^m = p

c)

m^t = p

d)

p^m = t

34.

Logarithmic functions are the inverse of...

a)

Linear Functions

b)

Exponential Functions

c)

Quadratic Functions

d)

Polynomial Functions

35.

x² = 16

a)

± 4

b)

± 8

c)

4

d)

8

36.

Evaluate $\sqrt[]{-10}$

a)

$i\sqrt[]{10}$

b)

$\sqrt[]{10}$

c)

10

d)

-10

37.

$i^2=$

(a)

38.

Which of the following quadratic equations can be solved easily by using extracting the square root?

a)

$x^2+3x-7=0$

b)

$x^2-10=0$

c)

$x^2+x=100$

d)

$x^2=x+10$

39.

Which of the following is Standard Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

40.

Which of the following is Vertex Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

41.

What is an equation of a parabola with the vertex of $\left(-2,-4\right)$ ?

a)

$y=-\left(x+2\right)^2-4$

b)

$y=\frac{3}{2}\left(x-2\right)^2+4$

c)

$y=\frac{3}{2}\left(x-2\right)^2-4$

d)

$y=\left(x+2\right)^2+4$

42.

Which of the following is Intercept (Factored) Form?

a)

$y=ax^2+bx+c$

b)

$y=a\left(x-p\right)\left(x-q\right)$

c)

$y=a\left(x-h\right)^2+k$

43.

What is an equation of a quadratic with x-intercepts at $\left(-1,0\right)$ and $\left(-10,0\right)$

a)

$y=-2\left(x+1\right)\left(x-10\right)$

b)

$y=\frac{1}{3}\left(x+1\right)\left(x+10\right)$

c)

$y=-\frac{1}{10}\left(x-1\right)\left(x+10\right)$

d)

$y=3\left(x-1\right)\left(x-10\right)$

44.

What is an equation of a quadratic with x-intercepts at $\left(7,0\right)$ and $\left(11,0\right)$

a)

$y=-\frac{1}{3}\left(x+7\right)\left(x-11\right)$

b)

$y=-\left(x+7\right)\left(x+11\right)$

c)

$y=\frac{2}{5}\left(x-7\right)\left(x+11\right)$

d)

$y=\frac{3}{2}\left(x-7\right)\left(x-11\right)$

45.

$y=-\frac{2}{3}\left(x-4\right)^2+10$ What is the vertex of the parabola with the equation

a)

$\left(4,10\right)$

b)

$\left(-4,10\right)$

c)

$\left(4,-10\right)$

d)

$\left(-4,-10\right)$

46.

a)

10

b)

-10

c)

10i

d)

-10i

47.

(5-2i) + (-7+8i)

a)

-2+6i

b)

12+6i

c)

-35-16i²

d)

-35 -16i

48.

What is the Degree of the Polynomial?

5x³ - 6x + 1

a)

1

b)

2

c)

3

d)

4

49.

What is the degree of the polynomial:

3x² + 9x⁵ − 4 + 10x⁸ + 2x⁹

a)

8

b)

9

c)

5

d)

-4

50.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

51.

Describe the degree and leading coefficient for the polynomial shown.

a)

Lead Coefficient: Positive

Degree: Even

b)

Lead Coefficient: Positive

Degree: Odd

c)

Lead Coefficient: Negative

Degree: Even

d)

Lead Coefficient: Negative

Degree: Odd

52.

In the above graph complete the following end behavior: (f(x)=y)
As x --> -∞, f(x) --> ____
As x --> +∞, f(x) --> ____

a)

-∞
-∞

b)

+∞
-∞

c)

-∞
+∞

d)

+∞
+∞

53.

Describe the end behavior of the graph.

a)

x → -∞, f(x) → ∞ and x→∞, f(x) →⁻∞

b)

x → -∞, f(x) → ∞ and x→∞, f(x) →∞

c)

x → -∞, f(x) → ∞ and x→∞, f(x) → 0

d)

x → -∞,f(x) → -∞and x→ ∞, f(x) → ∞

54.

What is the base in the expressions.

a)

3

b)

7

c)

-3

d)

-7

55.

Simplify

a)

b)

c)

d)

56.

Solve for x:
2^x+6=2⁵

a)

-1

b)

11

c)

1

d)

-11

57.

Solve the equation:

4^{x+3}=4^9

a)

x = 7

b)

x = 12

c)

x = 6

d)

x = 3

58.

Rewrite

\frac{1}{36}

as a power of 6.

a)

6

b)

$6^2$

c)

$6^6$

d)

$6^{-2}$

59.

Rewrite 64 as a power of 2:

a)

$2^2$

b)

$2^6$

c)

$4^3$

d)

$2^8$

60.

The table shows the x- and y- coordinates of some points on the graph of an exponential function.

Based on the table, which function represents the same relationship?

a)

$y=8\left(0.5\right)^x$

b)

$y=\left(0.5\right)^x$

c)

$y=0.5\left(8\right)^x$

d)

$y=8\left(1.5\right)^x$

1st semester Alg 2

Total questions: 60

Worksheet time: 2hrs 10mins

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