Quiz about Algebra 2L Spring Semester Review

Question 1

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

Accepted Answer

(4, 1) and (6, 4)

Answer

(1, 4) and (4, 6)

Answer

(-4, -1) and (-6, -4)

Answer

(-1, -4) and (-4, -6)

Question 2

The inverse has been reflected over which line?

Accepted Answer

y = x

Answer

y =1

Answer

y = 0

Answer

y = x + 1

Question 3

Is the inverse function found correctly?

Accepted Answer

yes

Answer

no

Question 4

In order for f(x) and g(x) to be inverse functions, which must be true of f(g(x)) and g(f(x))?

Accepted Answer

must equal x

Answer

must equal 1

Answer

must equal 0

Answer

must equal 2

Question 5

Identify the parent function of the graph.

Accepted Answer

Logarithmic

Answer

Rational

Answer

Exponential

Answer

Square Root

Question 6

Which of the following parent functions has a range of $$\left(0,\infty\right)$$

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 7

What type of function is shown?

Accepted Answer

exponential

Answer

linear

Answer

quadratic

Answer

square root

Question 8

What type of function is shown?

Accepted Answer

cube root

Answer

Exponential

Answer

square root

Answer

quadratic

Question 9

Find the inverse of f(x) = -4x - 12

Accepted Answer

f^-1(x) = -1/4x - 3

Answer

f^-1(x) = 4x - 3

Answer

f^-1(x) = 1/4x + 3

Answer

f^-1(x) = -4x - 3

Question 10

What is the equation for the red function?

Accepted Answer

g(x)=(x-1)³

Answer

g(x)=x3+1

Answer

g(x)=x3-1

Answer

g(x)=(x+1)³

Question 11

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

Accepted Answer

3 units left, 2 units up, reflected across the x-axis

Answer

3 units right, 2 units up, reflected across the y-axis

Answer

3 units right, 2 units up, reflected across the x-axis

Answer

3 units left, 2 units up, reflected across the y-axis

Question 12

$$\sqrt{x+9}=4$$

Accepted Answer

x = 7

Answer

x = -1

Answer

x = -7

Answer

x = 17

Question 13

Question 13.

Accepted Answer

x = 9

Answer

x = 2

Answer

x = 4

Answer

x = 7

Question 14

Which function represents the given graph?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 15

Solve the cube root equation

Accepted Answer

228

Answer

78

Answer

-228

Answer

-78

Answer

None

Question 16

Solve the cube root equation

Accepted Answer

344

Answer

21

Answer

-344

Answer

-21

Answer

None

Question 17

Solve: $$\sqrt[3]{x+10}=\sqrt[3]{4x+1}$$

Accepted Answer

3

Answer

4

Answer

no solution

Answer

1

Question 18

According to exponent rules, when we divide two powers with the same base we _______ the exponents.
Example: h⁸/h³

Accepted Answer

subtract

Answer

add

Answer

multiply

Answer

divide

Question 19

According to exponent rules, when we raise the power to a power we _______ the exponents.
Example: (d²)⁵

Accepted Answer

multiply

Answer

add

Answer

subtract

Answer

divide

Question 20

Simplify:

Accepted Answer

Option D is correct

Answer

A.

Answer

16c3d3

Answer

C.

Question 21

Simplify the expression.
x⁴ (x¹²)

Accepted Answer

x16

Answer

x3

Answer

x48

Answer

x8

Question 22

Simplify: $$\left(3x\right)^3$$

Accepted Answer

$$27x^3$$

Answer

$$9x^3$$

Answer

$$x^3$$

Answer

$$6x^3$$

Question 23

Simplify so there are no negative exponents in the answer.

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

Accepted Answer

$$x^5$$

Answer

$$\frac{1}{x^{18}}$$

Answer

$$-x^5$$

Answer

$$\frac{1}{x^{15}}$$

Question 24

What is the domain of the function in this graph?

Accepted Answer

[0, infinity)

Answer

(-infinity, 3]

Answer

[3, inifinity)

Answer

(-infinity, 0]

Question 25

What is the range of the function in this graph?

Accepted Answer

[3, infinity)

Answer

(-infinity, 3]

Answer

(-inifnity, 0]

Answer

[0 infinity)

Question 26

What is the DOMAIN of the function?

Accepted Answer

[-3, infinity)

Answer

[0, infinity)

Answer

[3, inifinity)

Answer

(-infinity, 0}

Question 27

What is the Domain of this exponential function?

Accepted Answer

All Real Numbers

Answer

y=1

Answer

x=0

Answer

x>0

Question 28

What is the Range of this function?

Accepted Answer

y> 0

Answer

x> 0

Answer

All Real Numbers

Answer

y= 1

Question 29

Logarithmic functions are the inverse of...

Accepted Answer

Exponential Functions

Answer

Linear Functions

Answer

Quadratic Functions

Answer

Polynomial Functions

Question 30

Find the domain and range of:
f(x) = log₂(x)

Accepted Answer

Domain: x > 0
Range: all real numbers

Answer

D: all real numbers
R: y > 0

Answer

Domain: all real numbers
Range: all real numbers

Answer

Domain: all real numbers
Range: y < 0

Question 31

What is an asymptote in the graph of a mathematical function?

Accepted Answer

A horizontal, vertical, or slanted line that a graph approaches but never touches.

Answer

Always a horizontal line that a graph approaches but never touches.

Answer

Always a vertical line that a graph approaches but never touches.

Answer

Always a slanted line that a graph approaches but never touches.

Question 32

Using the parent function $$y=\log_3x$$ what would the graph of $$y=\log_3\left(x+5\right)$$ look like?

Accepted Answer

Horizontal shift left 5 units

Answer

Horizontal shift right 5 units

Answer

Vertical shift up 5 units

Answer

Vertical shift down 5 units

Question 33

Solve: log₅25 = x

Accepted Answer

2

Answer

5

Answer

125

Answer

10

Question 34

What is the equation of the asymptote?

Accepted Answer

x = -3

Answer

x=5

Answer

y= -3

Answer

y=5

Question 35

Which equation is the inverse of the equation above?

Accepted Answer

Option A is correct

Answer

B.

Answer

C.

Answer

D.

Question 36

Rewrite in exponential form. $$\log_{6\ }t=m$$

Accepted Answer

$$6^m=t$$

Answer

$$m^t=6$$

Answer

$$t^m=6$$

Answer

$$6^t=m$$

Question 37

Rewrite the equation into logarithmic form:

6² = 36

Accepted Answer

log₆ 36 = 2

Answer

log₆ 2 = 36

Answer

ln 36 = 2

Answer

636 = 2

Question 38

Write in exponential form.
log₂32 = 5

Accepted Answer

25 = 32

Answer

2-5 = 32

Answer

232 = 5

Answer

325 = 2

Question 39

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

Accepted Answer

base.

Answer

exponent.

Answer

argument.

Answer

answer.

Question 40

Condense the expression to a single logarithm.
$$\log_{13}\left(x\right)-\log_{13}\left(y\right)$$

Accepted Answer

$$\log_{13}\left(\frac{x}{y}\right)$$

Answer

$$\log_{13}\left(xy\right)$$

Answer

$$\log_{13}\left(x^y\right)$$

Answer

$$\log_{13}\left(x-y\right)$$

Question 41

Condense the expression to a single logarithm.
$$\log_4\left(m\right)+\log_4\left(n\right)$$

Accepted Answer

$$\log_4\left(mn\right)$$

Answer

$$\log_4\left(\frac{m}{n}\right)$$

Answer

$$\log_4\left(m^n\right)$$

Answer

$$m\log_4\left(n\right)$$

Question 42

What is the horizontal asymptote?

Accepted Answer

y = 7

Answer

x = 2

Answer

x = 7

Answer

y = 2

Question 43

How is this function transformed from the parent function?

Accepted Answer

Translated right and down

Answer

Translated left and up

Answer

Translated right and up

Answer

Translated left and down

Question 44

What is the equation of the function seen here?

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 45

Find the vertical and horizontal asymptotes of $$f\left(x\right)=\frac{1}{x-3}+4$$

Accepted Answer

VA: $$x=3$$ HA: $$y=4$$

Answer

VA: $$x=-3$$ HA: $$y=4$$

Answer

VA: $$x=4$$ HA: $$y=3$$

Question 46

Identify the LCD.

Accepted Answer

x(x - 2)

Answer

x2(x - 2)

Answer

x

Answer

(x - 2)

Algebra 2L Spring Semester Review

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