Question 1

For the polynomial function, state the degree and leading coefficient.

Accepted Answer

Degree: 5
Leading Coefficient: 2

Answer

Degree: 3
Leading Coefficient: 4

Answer

Degree: 1
Leading Coefficient: 1

Answer

Degree: 2
Leading Coefficient: -3

Question 2

What is the end behavior of the function?

Accepted Answer

x → +∞,   y → +∞ and
x → -∞,   y → +∞

Answer

x → +∞,   y → -∞ and
x → -∞,   y → +∞

Answer

x → +∞,   y → -∞ and     
x → -∞,   y → -∞

Answer

x → +∞,   y → +∞ and
x → -∞,   y → -∞

Question 3

Perform the operation. $(8x^5-2x^2+5x)+(7x^5-x^2-9)$

Accepted Answer

$15x^5-3x^2+5x-9$

Answer

$1x^5-x^2+5x+9$

Answer

$15x^5-x^2+5x-9$

Answer

$15x^5-3x^2-9$

Question 4

Use the box method to  perform the operation. Write your answer in standard form. $(-x+4)(3x^2-2x+5)$

Accepted Answer

$-3x^3+14x^2-13x+20$

Answer

$3x^3+10x^2-10x+20$

Answer

$-3x^3+24x^2+40x+20$

Answer

$3x^3+14x^2+13x+20$

Question 5

Identify the mistake this student made when dividing the polynomials using synthetic division.

Accepted Answer

They should have added $1+2$ to get 3, but they multiplied $1 \cdot 2$ to get 2. There should be a remainder.

Answer

They should have put a negative 2 on the outside. You do not change the sign.

Answer

They should have changed the signs of the second row because they are subtracting.

Answer

They should have put a placeholder 0 in between the 1 and -4.

Question 6

Identify the number of solutions. $3x^6+4x^2-x+8$

Accepted Answer

6

Answer

2

Answer

5

Answer

3

Question 7

How many REAL solutions does the function have?

Accepted Answer

4

Answer

3

Answer

2

Answer

0

Question 8

If the equation of the function is $3x^6+4x^2-x+8$, then use the degree and the number of real zeroes to find the number of imaginary zeroes.

Accepted Answer

2

Answer

6

Answer

4

Answer

0

Question 9

Write a rule for $g$ that represents the indicated transformations on a graph of $f$. $f(x)=3x^4+5$, vertical stretch by a factor of 2 and a translation 5 units down, followed by a reflection in the y-axis.

Accepted Answer

$f(x)=6x^4$

Answer

$f(x)=\frac{3}{2}x^4$

Answer

$f(x)=3x^8+5$

Answer

$f(x)=6x^4+10$

Question 10

What is the index of the radical?
$(^7\sqrt{64})^5$

Accepted Answer

7

Answer

8

Answer

64

Answer

5

Question 11

Knowing $(^n\sqrt{a})^m=a^{\frac{m}{n}}$,  find the indicated real $n^{th}$ root(s) of $a$ if 
$n=5$ and $a=32$.

Accepted Answer

2

Answer

6

Answer

24

Answer

28

Question 12

Evaluate the expression: $81^{\frac{3}{4}}$

Accepted Answer

27

Answer

60.75

Answer

9

Answer

132,860

Question 13

State the domain and range of the function.

Accepted Answer

Domain: $x>3$
Range:$y>2$

Answer

Domain: $\mathbb{R}$
Range:$\mathbb{R}$

Answer

Domain: $x<3$
Range:$y<2$

Answer

Domain: $x>2$
Range:$y>3$

Question 14

Simplify the radical: $^4\sqrt{768}$

Accepted Answer

$4$$^4\sqrt{3}$

Answer

$16$$^4\sqrt{3}$

Answer

$4$

Answer

$16$$\sqrt{3}$

Question 15

A student made a mistake simplifying this radical. What mistake did they make?

Accepted Answer

When splitting up $y^8$, they should have added the exponents instead of multiplying them.

Answer

They forgot to write the radical in the answer.

Answer

The x that they took out of the radical should have been an $x^2$.

Answer

If there is no index, the number should be a 3.

Question 16

Change the expression with a rational exponent to a radical and evaluate. $(-128)^{\frac{3}{7}}$

Accepted Answer

-8

Answer

8

Answer

-244

Answer

55

Question 17

If there is no number on the bottom right side of a $log$, then what is the base?

Accepted Answer

10

Answer

2

Answer

5

Answer

1

Question 18

Choose the graph from the picture that best represents the function $f(x)=4e^{x+2}-3$

Accepted Answer

A

Answer

C

Answer

B

Answer

D

Question 19

Convert the equation from logarithmic form to exponential form. $log_{3}81=4$

Accepted Answer

$3^{4}=81$

Answer

$4^{81}=3$

Answer

$3^{81}=4$

Answer

$4^{3}=81$

Question 20

Convert the equation from exponential form to logarithmic form. $9^{\frac{3}{2}}=27$

Accepted Answer

$log_{9}27=\frac{3}{2}$

Answer

$log_{9}\frac{3}{2}=27$

Answer

$log_{27}9=\frac{3}{2}$

Answer

$log_{\frac{3}{2}}27=9$

Question 21

Evaluate the logarithm. $log_{2}64=$

Accepted Answer

6

Answer

19

Answer

32

Answer

16

Question 22

Describe the transformation of $f$ represented by $g$.
$f(x)=e^x$, $g(x)=e^{x-3}+2$

Accepted Answer

$g$ is a translation 3 units right and 2 units up of graph $f$.

Answer

$g$ is a reflection over the x-axis of graph $f$.

Answer

$g$ is a translation 2 units left and 3 units down of graph $f$.

Answer

$g$ is a translation 3 units left and 2 units up of graph $f$.

Question 23

Write a rule for $g$ that represents the indicated transformation of the graph of $f$. $f(x)=log_3x$; a reflection in the x-axis followed by a translation 1 unit up.

Accepted Answer

$g(x)=-log_{3}x+1$

Answer

$g(x)=-log_{3}(x+1)x$

Answer

$g(x)=log_{3}(-x)+1$

Answer

$g(x)=log_{3}(-x-1)$

Question 24

Expand the logarithmic expression.
Use the Properties if Logarithms:
$log_{b}(m \cdot n)=log_{b}m+log_{b}n$
$log_{b}(\frac{m}{n})=log_{b}m-log_{b}n$
$log_{b}(m^n)=n\cdot log_{b}m$

Accepted Answer

$log_{2}6+log_{2}x$

Answer

$6\cdot log_{2}x$

Answer

$log_{2}6-log_{2}x$

Answer

$log_{2}(6+x)$

Question 25

Condense the logarithmic expression.
Use the Properties if Logarithms:
$log_{b}(m \cdot n)=log_{b}m+log_{b}n$
$log_{b}(\frac{m}{n})=log_{b}m-log_{b}n$
$log_{b}(m^n)=n\cdot log_{b}m$

Accepted Answer

$log_{6}\frac{3}{x^4}$

Answer

$log_{6}(3\cdot x^4)$

Answer

$log_{6}x^{12}$

Answer

$log_{6}\frac{x^4}{3}$

Question 26

Solve the equation: $4^{5x+2}=4^{8x-4}$

Accepted Answer

$x=2$

Answer

$x=\frac{6}{13}$

Answer

$x=1$

Answer

$x=-\frac{2}{3}$

Question 27

Identify the A, B, and C in the following polynomial equation to factor using the ABC method. $x^2+10x-24$

Accepted Answer

A=1
B=10
C=-24

Answer

A=$x^2$
B=10
C=-24

Answer

A=1
B=10
C=24

Answer

A=$x^2$
B=10
C=24

Question 28

In the next step to factor the trinomial $x^2+10x-24$, find two numbers that will multiply to be $-24$ and add to be $+10$.

Accepted Answer

-2 and +12

Answer

4 and 6

Answer

-3 and -8

Answer

+2 and -12

Question 29

Find the zeroes (or solutions) of the trinomial.

Accepted Answer

$x=-12, 2$

Answer

$x=-2, 12$

Answer

$x=3, 8$

Answer

$x=-6, -4$

Question 30

Once you find the factors, what do you need to do to solve for the zeroes?

Accepted Answer

Set the factors equal to zero.

Answer

Combine like terms.

Answer

Multiply them out using the box method.

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