Quiz about PC Chapter 3 Mid Review: Exponential & Logarithmic Functions

Question 1

Describe the transformation that results in the graph of g(x) from f(x).

$$f\left(x\right)=\left(\frac{3}{2}\right)^{x\ }$$ and $$g\left(x\right)=\left(\frac{3}{2}\right)^{-x}$$

Accepted Answer

Reflected over the y axis

Answer

Reflected over the x axis

Question 2

Describe the transformation that results in the graph of g(x) from f(x).

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

Choose all that apply!

Accepted Answer

Horizontal shift right by 2

Accepted Answer

Vertical Stretch by 2

Answer

Horizontal shift left by 2

Answer

Vertical Contraction by 2

Answer

Vertical shift down by 2

Question 3

Describe the transformation that results in the graph of g(x) from f(x).

$$f\left(x\right)=e^x$$ and $$g\left(x\right)=-e^x-6$$

Choose all that apply!

Accepted Answer

Vertical shift down by 6

Accepted Answer

Reflection over the x axis

Answer

Vertical shift up by 6

Answer

Horizontal shift left by 6

Answer

Reflection over the y axis

Question 4

Describe the transformation that results in the graph of g(x) from f(x).

$$f\left(x\right)=10^x$$ and $$g\left(x\right)=10^{2x}$$

Accepted Answer

Horizontal Contraction by 1/2

Answer

Horizontal shift left by 2

Answer

Horizontal shift right by 2

Answer

Horizontal Expansion by 2

Answer

Vertical Contraction by 1/2

Question 5

In the formula for compound interest, $$A=P\left(1+\frac{r}{n}\right)^{nt}$$ , which variable has NO effect on the amount of time it takes an investment to double?

Accepted Answer

P

Answer

r

Answer

n

Answer

t

Question 6

Find the balance in the account after the given period.

$5000 deposit earning 1.5% compounded quarterly after 3 years

Accepted Answer

$5,229.70

Answer

$7,604.38

Answer

$7,777.27

Answer

$5,538.86

Question 7

The graph of $$f\left(x\right)=\log_2x$$ contains the given point (4,1) and has the vertical asymptote shown.

Which of the following is the function for the graph?

Accepted Answer

$$f\left(x\right)=\log_2\left(x+3\right)+1$$

Answer

$$f\left(x\right)=\log_2\left(x-4\right)+1$$

Answer

$$f\left(x\right)=-\log_2\left(x-3\right)+1$$

Answer

$$f\left(x\right)=\log_2\left(x-3\right)+1$$

Question 8

Expand the logarithm

$$\log_7\frac{2}{3}$$

Accepted Answer

$$\log_7\left(2\right)-\log_7\left(3\right)$$

Answer

$$\log_7\left(3\right)-\log_7\left(2\right)$$

Answer

$$\log_7\left(2\right)+\log_7\left(3\right)$$

Answer

$$3\log_7\left(2\right)$$

Question 9

Expand the logarithm:

$$\log\left(\frac{8x}{yz}\right)\ $$

Accepted Answer

log(8)+log(x)-log(y)-log(z)

Answer

log(8)+log(x)-log(y)+log(z)

Answer

log(8x)-log(yz)

Answer

8log(x)-ylog(z)

Question 10

Which expression is equivalent to $$\log_2\left(\frac{m^4}{n^7}\right)$$

Accepted Answer

$$4\log_2m-7\log_2m$$

Answer

$$4\log_2m+7\log_2m$$

Answer

$$7\log_2m+4\log_2m$$

Answer

$$7\log_2m-4\log_2m$$

Question 11

Write as a single logarithm:

log(30) - log(6)

Accepted Answer

log(5)

Answer

-6log(30)

Answer

log(24)

Answer

log(-24)

Question 12

Condense the logarithm:

$$\log_43+\log_45$$

Accepted Answer

$$\log_415$$

Answer

$$\log_4\frac{3}{5}$$

Answer

$$\log_4\frac{3}{2}$$

Answer

$$\log_4\frac{5}{3}$$

Question 13

Which of the following is NOT equivalent to $$\log_216$$

Accepted Answer

All of these are equivalent

Answer

$$4\log_22$$

Answer

$$\log_28+\log_22$$

Answer

$$\log_264-\log_24$$

Answer

$$\log_2160-\log_210$$

Question 14

Evaluate: $$\log_3\left(27\right)^2$$

Accepted Answer

6

Answer

5

Answer

3

Answer

9

Question 15

Which graph matches the equation:

$$f\left(x\right)=2\left(3\right)^x+6$$

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 16

Which equation matches this graph?

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

PC Chapter 3 Mid Review: Exponential & Logarithmic Functions

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