Free Printable Math 3 Final Review

1.

$f\left(x\right)=\frac{x}{5}+3$
What is the inverse, $f^{-1}\left(x\right)$ ?

a)

$f^{-1}\left(x\right)=5x-3$

b)

$f^{-1}\left(x\right)=5\left(x-3\right)$

c)

$f^{-1}\left(x\right)=5x+3$

d)

$f^{-1}\left(x\right)=5\left(x+3\right)$

2.

Mark ALL the properties of inverse functions.

a)

The equations contain the inverse operations in the reverse order.

b)

The graphs of the two functions are refelections of each other in the line y = x.

c)

The domain of one function is the range of the other function.

d)

The range of one function is the domain of the other function.

e)

If $f\left(a\right)=b,\$ the $f^{-1}\left(b\right)=a$ .

3.

If the domain of f(x) is all real numbers, then

a)

the range of f(x) is all real numbers.

b)

the range of the inverse of f(x) is all real numbers.

c)

Both are true.

d)

Neither are true.

4.

If $f(x)=\log_x⁡11$ , then

a)

$f^{-1}(x)=11^x$

b)

$f^{-1}(x)=x^{11}$

c)

$f^{-1}(x)=11x$

d)

None of the above

5.

$\log_33$

a)

-2

b)

-1

c)

0

d)

1

e)

2

6.

$\log_3\left(\frac{1}{9}\right)$

a)

-2

b)

-1

c)

0

d)

1

e)

2

7.

Choose which describes the translation of the graph of $f(x)=\log_5⁡x$ on to the graph of $f(x)=-4+\log_5⁡\left(x-1\right)$ .

a)

up 4 units right 1 unit

b)

up 4 units left 1 unit

c)

down 4 units right 1 unit

d)

down 4 units left 1 unit

8.

$(2x^2−8)−(x^2-4x-3)$

a)

$x^2+4x-5$

b)

$x^2+5x+5$

c)

$-x^2-4x+5$

d)

$x^2-4x-11$

9.

$(2x−1)(x-3)$

a)

$2x^2+7x-3$

b)

$2x^2-7x-3$

c)

$2x^2+7x+3$

d)

$2x^2-7x+3$

10.

Which function has 4 roots?

a)

$f\left(x\right)=5x^4$

b)

$f\left(x\right)=4x^3$

c)

$f\left(x\right)=-8x^2$

d)

none of the above

11.

Match the graph to the function

a)

f(x)= -x²+3x+2

b)

f(x) = -x³+2

c)

f(x) = x³+2

d)

f(x) = ⅓x⁴-5x²+2

12.

What is another way to say "where a function crosses the x-axis"?

a)

x-intercept

b)

zero

c)

root

d)

all of these.

13.

What are the zeros of the function?

a)

4,1

b)

3,1,-2,-5

c)

-3, -1, 2, 5

d)

-2,4

14.

Write the cubic polynomial in factored form with
zeros -1, 1, and 4

a)

(x + 1) (x - 1) (x - 4)

b)

x³ - 4x² - x + 4

c)

(x + 1) (x - 1) (x + 4)

d)

x³ - 4x² - x - 4

15.

Which polynomial is in standard form?

a)

2 + x + 4

b)

x⁴ + x⁷

c)

2 + x² + 3x

d)

2x³ + 3x² + x + 4

16.

A logarithm is the inverse function of

a)

a quadratic.

b)

an exponential.

c)

a linear function.

d)

a cubic.

17.

In the equation $\log_8\left(2\right)=\frac{1}{3}$ , 8 is the:

a)

base.

b)

exponent.

c)

argument.

d)

answer.

18.

Rewrite the equation in exponential form.
$\log_8\left(512\right)=3$

a)

$8^{512}=3$

b)

$3^8=512$

c)

$8^3=512$

d)

$3^{512}=8$

19.

Rewrite the equation in logarithmic form.
$5^{-4}=\frac{1}{625}$

a)

$\log_5\left(-4\right)=\frac{1}{625}$

b)

$\log_5\left(\frac{1}{625}\right)=-4$

c)

$\log_{-4}\left(\frac{1}{625}\right)=5$

d)

$\log_{\frac{1}{625}}\left(5\right)=-4$

20.

Rewrite the equation in exponential form.
$\log_{12}\left(w\right)=p$

a)

$12^w=p$

b)

$12^p=w$

c)

$w^p=12$

d)

$p^w=12$

21.

Evaluate the expression:
$\log_3\left(81\right)$

a)

4

b)

27

c)

78

d)

5

22.

Evaluate the expression:
$\log_4\left(\frac{1}{64}\right)$

a)

3

b)

$-3$

c)

$\frac{1}{3}$

d)

16

23.

Given $f\left(x\right)\ =\ \left(x\ -\ 3\right)^3$ describe the shift from the parent function $f\left(x\right)\ =\ x^3$

a)

up 3

b)

down 3

c)

left 3

d)

right 3

24.

Given $f\left(x\right)\ =\ \left(x\ +\ 2\right)^3$ describe the shift from the parent function $f\left(x\right)\ =\ x^3$

a)

up 2

b)

down 2

c)

left 2

d)

right 2

25.

Given $f\left(x\right)\ =\ x^3\ +\ 4$ describe the shift from the parent function $f\left(x\right)\ =\ x^3$

a)

up 4

b)

down 4

c)

left 4

d)

right 4

26.

Given $f\left(x\right)\ =\ x^3\ -5$ describe the shift from the parent function $f\left(x\right)\ =\ x^3$

a)

up 5

b)

down 5

c)

left 5

d)

right 5

27.

Select the equation of the graph pictured above

a)

$f\left(x\right)\ =\ x^3\ -\ 2$

b)

$f\left(x\right)\ =\ x^3\ +\ 2$

c)

$f\left(x\right)\ =\ \left(x\ +\ 2\right)^3$

d)

$f\left(x\right)\ =\ \left(x\ -\ 2\right)^3$

28.

What would the equation of the graph be for $f\left(x\right)\ =\ x^3$ shifted up 3 and left 4

a)

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

b)

$f\left(x\right)\ =\ \left(x\ +\ 4\right)^{2\ }+3$

c)

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

d)

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

29.

What would the equation of the graph be for $f\left(x\right)\ =\ x^3$ shifted down 1 and right 4

a)

$f\left(x\right)\ =\ \left(x\ -\ 4\right)^{2\ }-1$

b)

$f\left(x\right)\ =\ \left(x\ +\ 4\right)^{2\ }+1$

c)

$f\left(x\right)\ =\ \left(x\ +\ 4\right)^{2\ }-1$

d)

$f\left(x\right)\ =\ \left(x\ -\ 4\right)^{2\ }+1$

30.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

31.

Perform the indicated operation . Write answer in descending order

(3x^2-8x+7)+(8x^2+9x-16)

a)

$11x^4+x^2-9$

b)

$11x^2-x-9$

c)

$11x^2-17x-11$

d)

$11x^2+x-9$

32.

Perform the indicated operation. Write answer in descending order.

(8x^2-12x+6)+(7x^3+8x-15)

a)

$15x^2-4x-9$

b)

$7x^3+8x^2-4x-11$

c)

$7x^3+8x^2-4x-9$

d)

$15x^2-4x-11$

33.

Perform the indicated operation.

Write answer in descending order.

( 9x² - 7x + 8 ) - ( 12x² - 8x - 11 )

a)

-3x² - 15x + 19

b)

21x² - 15x - 3

c)

-3x² - 15x - 3

d)

-3x² + x + 19

34.

Perform the indicated operation.

Write answer in descending order.

( 18x² - 13x - 8 ) - ( -7x² - 9x - 17 )

a)

9x² - 22x - 25

b)

25x² - 4x + 9

c)

25x² - 22x + 9

d)

25x² - 4x - 25

35.

(5x+2)(x²-3x+6)

a)

5x³- 17x²+24x +12

b)

5x³+ 17x² - 24x +12

c)

5x³ - 13x² + 24x +12

d)

5x³ +13x² - 24x - 12

36.

Simplify:
(3x-5) (4x²-2x-3)

a)

12x³ - 26x² - 25x + 15

b)

12x³ - 20x² - 5x + 15

c)

12x³ - 20x² - 6x + 15

d)

12x³ - 26x² + x + 15

37.

Given the polynomial below, how many roots will it have?
$y=x^3+5x^2-9x-2$

a)

2

b)

1

c)

3

d)

0

38.

What are the roots of the polynomial?

a)

-3, 0, and 3

b)

0

c)

-2, 10, and -10

d)

11, 0 and -11

Math 3 Final Review

Total questions: 38

Worksheet time: 48mins

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