Exponential Functions and Transformations

​Key Features of Exponential Functions

Today, we will learn what an exponential function is and what its key features are.​

If b is...

• Greater than 1 (b>1), the function is exponential GROWTH

• Less than 1 and greater than 0 (0<b<1) the function is exponential DECAY

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​Definition of exponential function

​Growth vs Decay

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Domain: all possible x values

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​D= all real numbers

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Range: all possible y values

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R= y>0​

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Asymptote: Imaginary line that the graph approaches, but never crosses​

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y=0​

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​PARENT FUNCTION ONLY

​Key Features

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Y- Intercept: one y-intercept

​The y-intercept is "a"

y-intercept=1​

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X- Intercept​​: NO x-intercepts

​PARENT FUNCTION ONLY

​Key Features

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Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay

Multiple Choice

Is the following function an example of decay or growth?

f(x) = 2(1.25)^x

• Exponential Growth

• Exponential Decay

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay

Multiple Choice

Which represents exponential decay?

• A

• B

• C

• D

Multiple Choice

What is the domain of the function shown?

• All real numbers

• $$y>0$$  

• All real numbers greater than 1

• $$y<0$$  

Multiple Choice

What is the range of the exponential function?

• all real numbers

• y > -1

• y < -1

• x > -1

Multiple Choice

What is the y-intercept of the function?

• 2
• 3
• 1
• -2

Multiple Choice

In an exponential function, what does the 'a' represent? 

• SLOPE
• RATE OF CHANGE
• Y-INTERCEPT
• COMMON RATIO

Multiple Choice

What is the equation of the horizontal asymptote for following exponential function?

• y = -4

• y > -4

• y < -4

• (0, -3)

Exponential Functions & Transformations

Transformations

• Shifts

• Stretches

Multiple Choice

What type of function is

$$f\left(x\right)=2\cdot\left(\frac{1}{7}\right)^x$$ ? 

• Exponential Growth

• Linear

• Exponential Decay

• None of the Abovee

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

• Growth

• Decay

Multiple Choice

What type of pattern do exponential functions have?

• Adds by the same number every time

• Multiplies by the same number every time

• Square roots all the inputs

• Squares all the inputs

Multiple Choice

What type of pattern do linear functions have?

• Adds by the same number every time

• Multiplies by the same number every time

• Square roots all the inputs

• Squares all the inputs

Multiple Choice

Is the graph linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Is the graph linear, exponential or neither?

• Linear

• Exponential

• Neither

Multiple Choice

In an exponential function, what does the 'a' represent?

• Slope

• Rate of change

• Y-intercept

• Multiplier

Multiple Choice

In an exponential function, what does the 'b' represent?

• Slope

• Rate of change

• Y-intercept

• Multiplier

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Neither

Multiple Choice

Is the table linear, exponential, or neither?

• Linear

• Exponential

• Nether

Multiple Choice

What is the domain of the function shown below?

• -2 < x < 5

• 0 < x < 12

• y > 0

• All Real Numbers

Multiple Choice

What is the range of the function shown below?

• 0 < y < 12
• -2 < y < 5
• y > 0
• All Real Numbers 

Multiple Choice

Determine the horizontal asymptote for the function

f(x) = 3(2)^x-4 + 5

• x=4

• y=4

• x=5

• y=5

Multiple Choice

Does this table represent exponential growth or decay?

• Growth

• Decay

Multiple Choice

Which function represents the table of values?

• f(x) = 4x

• f(x) = x⁴

• f(x) = 4^x

• f(x) = 4^x-1

Multiple Choice

Determine the range for the function

f(x) = 3(2)^x-4 + 5

• [5,∞)

• (5,∞)

• [4,∞)

• (4,∞)

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.

A=1200(.85)⁶

• Growth

• Decay

Multiple Choice

For $$y=a\left(b\right)^x+k$$ , how does adding a constant transform the parent function?

• Horizontal shift

• Vertical Shift

• Reflection over the x-axis

• Reflection over the y-axis