Exponential and Logarithmic Functions - Study Guide

​As you go through this Quizizz lesson, you are creating your own study guide to use on the test. If you see this icon,











it means write down the information on that slide!!!

Exponential Functions have a variable in the exponent

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Exponential Functions

f(x) = a (b)^x

^{a = initial value or starting amount}

^{b= (common ratio) growth or decay factor}

Multiple Choice

What is the initial value in y=4(2)^x

• 4

• 2

• x

Multiple Choice

What is the y-intercept in y=4(2)^x

• (4,0)

• (0,2)

• x

• (0,4)

• (4,2)

Multiple Choice

What is the starting amount in the problem below?

f(t) = 300(1.05)^t

• 300

• 1.05

• t

• y

Multiple Choice

What is the common ratio for the function f(x) = 25 (4)^x

• 25

• 4

Exponential Growth and Decay

Growth vs. Decay

• If b > 1 then growth

• If 0<b<1, then decay

Both Graphs have a

Horizontal Asymptote

(graph never touches

the X-axis)

b^x cannot equal 0

Growth Function

The constant multiplier is bigger than 1, meaning the starting value is keeping 100% of its value and adding some percent.

Decay Function

The constant multiplier is between 0 and 1. This number comes from subtracting the decay rate from 100% of the original starting value.

Multiple Select

Which of these functions is a growth function? Check all that apply.

• $$f\left(x\right)=7\left(1.2\right)^x$$

• $$f\left(x\right)=5\left(0.8\right)^x$$

• $$f\left(x\right)=0.5\left(3\right)^x$$

• $$f\left(x\right)=3\left(\frac{4}{3}\right)^x$$

Multiple Choice

What is the decay RATE of this function?

$$f\left(x\right)=100\left(0.85\right)^x$$  

• 100

• 0.85

• 0.15

• $$\left(1-0.15\right)$$  

Multiple Choice

The population of Bloom Falls, Mass. (population 937) is slowly moving to a bigger city.
Every year the population drops by 4.5%. What is the population after 3 years?

• 1,069 people

• 894 people

• 816 people

• 854 people

Multiple Choice

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

• $5,884.00

• $5,178.97

• $2,992.96

• $2,957.04

Multiple Choice

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^t where t is the number of years since 1990. What was the population in 1990? 

• 0 people

• It doesn't say

• I don't know

• 6191

Multiple Choice

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1400(1.09)^x

• y=1.09(1400)^x

• y=1400(.91)^x

• y=1.09^x

Multiple Choice

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

• $33,299.42

• $33,672.68

• $34,157.04

• $34,710.88

Multiple Choice

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

• $6,273.50

• $6,314.08

• $6,385.72

• $6,427.94

Multiple Choice

Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent?

• $613.40

• $6,136.40

• $61,364

• $613,640

Graphing Exponential Equations

Multiple Choice

if $$y=2^x$$   what is y when x = 0, 2, 4?

• 1, 2 and 8

• 1, 4 and 16

• 0, 4 and 8

• 1, 2 and 8

Multiple Choice

What is the domain of the function shown below?

• (-2,5)

• (0,12)

• $$\left(0,\infty\right)$$  

• All Real Numbers

Graphing

Graph $$y=3^x$$

Graphing

Graph $$y=3^x-2$$

Graphing

Graph $$y=3^{x-2}$$

Logs are the inverse of Exponential Functions--their graphs are inverted

2^x is in red

log₂​ x is in blue

Notice the asymptotes?​

​

​What else has switched?

​

Graphs of Log Functions

​To Graph a Log Function:

1. ​Make a table for the inverse function

2. Flip all the points

Multiple Choice

Identify the asymptote of the transformed graph $$\log_2\left(x+3\right)$$  shown in red in the graph

• $$x=-3$$  

• $$x=3$$  

• $$y=3$$  

• $$y=-3$$  

Multiple Choice

Which of the equations could best describe the graph?

• $$\log_2\left(x+1\right)$$  

• $$\log_2\left(x-1\right)$$  

• $$\log_2\left(x\right)+1$$  

• $$\log_2\left(x\right)-1$$  

Match

Match the following log functions to their horizontal shift (which way will the asymptote shift)

• $$\ln\left(x\right)$$  

• $$\ln\left(x-4\right)$$  

• $$\ln\left(x+5\right)$$  

No Horizontal Shift

Shift Right

Shift Left

• No Horizontal Shift

• Shift Right

• Shift Left

Multiple Choice

Identify the asymptote for the function ℎ(𝑥) = 𝑙𝑛(𝑥 − 1) + 3.

• $$x=3$$  

• $$x=-1$$  

• $$y=1$$  

• $$x=1$$  

Multiple Choice

Which graph correctly shows the asymptote of $$f(x)=\log(x+2)+3$$  

Domain: x > -2

​h will affect the domain of log functions

​

​Remember: can't take the log of ZERO or NEGATIVE arguments

​

The vertical asymptote is either the left or right boundary of domain​​

Match

Match the following graphs with their domains

Domian: x > -2

Domian: x > 3

Domian: x > 0

Domian: x > 2

• Domian: x > -2

• Domian: x > 3

• Domian: x > 0

• Domian: x > 2

Review

Match

Match each equation in logarithmic form to the corresponding exponential form.

• $$\log_2 8 = x$$

• $$\log_5 125 = x$$

• $$\log_2x=8$$

• $$\log_4 64 = x$$

• $$\log_5x=125$$

• $$2^x = 8$$

• $$5^x = 125$$

• $$2^8=x$$

• $$4^x = 64$$

• $$5^{125}=x$$

​Properties of Logs

Multiple Choice

Expand

log(4x)

• log4-logx

• log4+logx

• 4logx

• xlog4

Multiple Choice

Expand

log(xy²)

• logx+2logy

• logx+logy²

• logx-2logy

• logx+logy+log2

Multiple Choice

$$Expand\ \log\left(\frac{x}{y}\right)$$  

• logx+logy

• xlogy

• log(x-y)

• logx-logy

Multiple Choice

• log (xy³)
• log (x⁶ − y³)
• log (x⁶/y³)
• log (x⁶ + y³)

Multiple Choice

Write as a single log: log 12 + 2⋅log x

• log (12 + 2x)

• log (14x)

• log (12 * 2x)

• log (12x²)

Multiple Choice

Using the change of base property, rewrite log₂31

• log(2) / log(31)

• log(2/31)

• log(31)/log(2)

• log(31/2)

Remember - our test will also include

• using logs to solve exponential equations

• using exponentials to solve logarithmic equations

Refer to the notes we worked on yesterday for those topics!