Exponential Functions & Shifts

Exponential Functions & Shifts

Domain, Range, Growth, Decay, and Transformations

Domain & Range of Functions

Domain--set of all x-values (For any function, the domain is __________)

Range--set of all y-values (For exponential functions, we look at the ___________ to determine our range.)

Multiple Choice

(Click on the image to enlarge, and then select the correct answer.)

• A

• B

• C

• D

Multiple Choice

What is the range of this graph?

• y = 6
• (0, -4)
• y > -6
• y < -6

Multiple Choice

What is the domain of this graph?

• x = -10

• $-\infty\le x\le\infty$

• x>0

• x < 10

Multiple Choice

What is the y-intercept of the function?

• 2
• 3
• 1
• -2

Exponential vs. Linear Lesson: Growth and Decay

I can determine if a function is modeling growth or decay.

I can create a table for a function.

I can evaluate a function.

Positive Rate of Change

• Previously, we've discussed how linear functions are increasing when they go upward from left to right on a graph

• We also know a linear function if its m-value (slope) is positive

Negative Rate of Change

• Previously, we've discussed how linear functions are decreasing when they go downward from left to right on a graph

• We also know a linear function if its m-value (slope) is negative

Poll

Exponential functions use the terms "growth" and "decay" instead. Which of the two graphs do you think is "growing" from left to right, and could be labeled "growth"? Click on your choice.

Multiple Choice

Is the graph linear, exponential or neither?

• Linear
• Exponential
• Neither

Multiple Choice

Which of the graphs is exponential decay?

Multiple Choice

Is the pictured graph growth, decay, or linear or quadratic?  

• Growth
• Decay
• Linear
• Quadratic

Multiple Choice

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

• Exponential Growth
• Exponential Decay
• Linear
• None

Multiple Choice

Is the pictured graph growth, decay, or linear or quadratic?  

• Growth
• Decay
• Linear
• Quadratic

Multiple Choice

Is the pictured graph growth, decay, or linear or quadratic?

• Growth

• Decay

• Linear

• Quadratic

Multiple Choice

Which represents exponential decay?

• A

• B

• C

• D

Shifts of Exponential Functions

• Parent Function:

•  $y=b^x\$  

• The asymptote is at 0, and there is no movement along the x-axis or y-axis (h = 0, and k = 0, a = 1)

Multiple Choice

What kind of shift  is represented?

• up 1 unit
• left 1 unit
• right 1 unit 
• down 1 unit

Multiple Choice

What kind of shift happens with this function?

• 4 points up
• 4 points to the left
• 4 points to the right
• 4 points down

Multiple Choice

What is the transformation?

• Vertical Translation up 2 and Horizontal translation right 1
• Vertical Translation down 2 and Horizontal Translation left 1
• Horizontal Translation left 2 and Vertical Translation up 1
• Horizontal Translation right 2 and Vertical Translation down 1

Multiple Choice

What is the transformation?

• Vertical Translation up 2
• Vertical Translation down 2
• Horizontal Translation left 2
• Horizontal Translation right 2

Multiple Choice

What transformations occur in the following function?

• right 3, up 2

• left 3, up 2

• left 3, down 2

• right 3, down 2

Multiple Choice

What is the transformation?

• Vertical Translation up 1
• Vertical Translation down 1
• Horizontal Translation left 1
• Horizontal Translation right 1