Exponential Functions Review

Talk to me

100

Explain what an exponential growth would look like.

Goes up at a non-constant fast rate of change.

250

Explain what an exponential decay would look like.

Goes down at a non-constant fast rate.

475

Why do some exponential graphs look like a "swoosh" and others look like a "squiggly S" kind of shape?

A "swoosh" is from an exponent of x.

A "squiggly S" is from an exponent of 3 or higher.

800

What is the hardest thing for you with exponential functions?

Any appropriate answer is correct. IDK or similar is not valid.

1750

What are 3 specific differences between a Linear function and an Exponential function?

Linear: Constant rate of change, perfectly straight line, exponent of an imaginary 1, y=mx+b

Exponential: Non-constant rate of change, "swoosh" or "squiggly S" shape, exponent of 3 or higher, exponent can be an x, f(x)=a^x 

Prove it

100

If  f(x)=  - 2^x + 3 then f(7)=____

f(7)= - 125

250

If  f(x)=  15^x  then f(1)=____

f(1)=15 

475

If  f(x)=  X^x + 4 then f(-1)=____

f(-1)= 3

800

Graph f(x)= 2^x - 7

Image Unavailable

1750

Graph f(x)= 0.5^x 

Image Unavailable

Detective

100

Growth or Decay

f(x) = 6^x - 3

Growth

250

 On an island, a rare breed of rabbit doubled its population each month for two years. 

1. Exponential Growth          2. Linear Growth

3. Exponential Decay           4. Linear Decay

Exponential Growth

475

Which scenario represents exponential growth? 

1. A car increases its distance from a garage as it travels at a constant speed of 25 miles per hour.

2. A vine grows 6 inches every week.

3. A species of fly doubles its population every month during the summer.

3. A species of fly doubles its population every month during the summer.

800

If  f(x)=  - X^x then f(0)=____ . Then state what it that means when you are graphing.

f(0)= ERROR which means that you would have an open circle on your graph to represent the value missing. 

AKA: Just like you do for graphing inequalities!

1750

Which equation represents an exponential decay with a constant value of 3. 

f(x)= - 2^x - 3                  g(x)=  - 2^x + 3

h(x)= - 3^x - 2                  j(x)= - 3^x + 2

 g(x)=  - 2^x + 3

Vocabulary

100

State at least 2 specific facts about any function

Pass the VLT, only one input for each output, X values can't repeat

250

Non-constant rate of change

Exponential function

475

Process to find rate of change on a table

Find the difference of Y₂ and Y₁ & X₂ and X_1. 

_{AKA: Subtract the values on the table to find the slope.}  

800

What does an exponential equation look like?

f(x)=a^x    or     f(x)=ax^x

1750

What is the difference between a Domain and a Range?

Domain is the X values and Range is the Y values.