Exponential Functions

Multiple Choice

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

f(x) = a ⋅ b^x

• Asymptote

• y -intercept

• x-intercept

• Multiplier

Multiple Choice

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

f(x) = a ⋅ b^x

• Asymptote

• y -intercept

• x-intercept

• Multiplier

Multiple Choice

In an exponential function, what is an interpretation of the y-intercept?

• initial amount

• ending amount

• growth factor

• decay factor

Multiple Choice

Find the y-intercept

• y=1

• y=-2

• y=3

• y=2

Open Ended

Explain how you can determine whether each equation represents growth or decay.

Open Ended

Explain how you can determine how to find the multiplier.

Open Ended

Explain how you can determine how to find the y-intercept.

Multiple Choice

Which of the following best describes a horizontal asymptote in the context of exponential functions?

• A line that the graph approaches but never touches

• A line that the graph crosses infinitely many times

• A line that the graph always stays above

• A line that the graph intersects at one point

Multiple Choice

Every Exponential Function has an asymptote.

• Sometimes

• Always

• Never

Multiple Choice

The asymptote is the highest or lowest point in the graph Exponention function

• Always

• Sometimes

• Never

Multiple Choice

What is the asymptote of y = 2^x ?

• y = 0

• x = 0

Multiple Choice

What is the asymptote of y = 2^x - 3

• y = 0

• y = -3

• x = 0

• x = -3

Multiple Choice

Which of the following statements best captures the meaning of an asymptote for an exponential function?

• It is a horizontal line that the graph approaches, but never touches.

• It is a vertical line that the graph approaches, but never touches.

• It is a horizontal line that intersects the graph of the function.

• It is a vertical line that intersects the graph of the function.

Multiple Choice

Based on the given graph, what is the equation for the asymptote? Choose the best answer.

• y = 1

• x = 1

• y = 2

• x = 0

Multiple Choice

Which of the following equations may be used to represent the asymptote shown in the graph?

• y = -2

• x = -2

• y = -1

• x = 5

Multiple Choice

Find the aymptote

• x=1

• y=1

• y=-1

Multiple Choice

Find the Asymptote

• y=0

• x=0

• y=1

• x=1

Multiple Choice

Find the asymptote

• y=4

• x=4

• None

Multiple Choice

What is the asymptote of the exponential function shown here?

• y = 4

• y = 3

• x = 4

• x = 3

Multiple Choice

What is the horizontal asymptote of this graph?

• y = -2

• y = 2

• y = 1

• y = -1

Multiple Choice

Select the color of the line that represents the asymptote of the graph shown.

• Purple

• Blue

• Green

• Red

Multiple Choice

Given the table of values for x and y, what is the correct exponential function in the form y = a(b)ˣ?

• y = 32(0.75)ˣ

• y = 24(0.75)ˣ

• y = 10(0.75)ˣ

• y = 24(2.5)ˣ

Multiple Choice

Given the graph for x and y, what is the correct exponential function in the form y = a(b)ˣ?

• y = 10(2.5)ˣ

• y = 25(10)ˣ

• y = 5(1/2)ˣ

• y = 10(.25)ˣ

Multiple Choice

Given the table of values for x and y, what is the correct exponential function in the form y = a(b)ˣ?

• y = 8(1/4)ˣ

• y = 4(8)ˣ

• y = 32(4)ˣ

• y = 8(4)ˣ

Multiple Choice

Which equation accurately matches the table?

• y = 16(1.25)ˣ

• y = 20(1.25)ˣ

• y = 20(0.75)ˣ

Multiple Choice

Which equation accurately matches the graph?

• y = 20(2)ˣ

• y = 20(0.5)ˣ

• y = 0.5(20)ˣ

Multiple Choice

Which equation accurately matches the graph?

• y = 12(1/3)ˣ

• y = 12(-1/3)ˣ

• y = 12(2)ˣ

Multiple Choice

Which equation accurately matches the table?

• y = -3(2)ˣ

• y = -2(12)ˣ

• y = -12(2)ˣ

Multiple Select

Select all equations that correctly represent exponential decay from the options provided for the graphs and tables.

• y = 20(0.5)^x

• y = 12(1/3)^x

• y = 20(2)^x

• y = 16(1.25)^x

Open Ended

Selah and Carson each made a mistake when writing equations for the representations below. Describe one possible mistake Selah made.

Multiple Choice

Choose the correct equation for Selah's graph.

• y = 3ˣ

• y = 2(3)ˣ

• y = 6(2)ˣ

• y = 3(2)ˣ

Open Ended

Selah and Carson each made a mistake when writing equations for the representations below. Describe one possible mistake Carson made.

Multiple Choice

Choose the correct equation for Carson's graph.

• y = 16(4)ˣ

• y = 4(64)ˣ

• y = 64(1/4)ˣ

• y = 3(4)ˣ

Fill in the Blanks

Fill in the Blanks

Multiple Choice

is the exponential equation for this table

y = 80 (1.5)ˣ

• yes

• no

Multiple Choice

Which graph is representative of the equation?

Multiple Select

Which of the following equations represents exponential decay?

• y = 3(4)ˣ

• y = 4(1/2)ˣ

• y = 3(1.03)ˣ

• y = 3(0.5)ˣ

Multiple Choice

The graph of an exponential function is given. What is the domain of this function?

• All real numbers.

• All real numbers greater than zero.

• All real numbers less than zero.

• All real numbers greater than one.

Multiple Choice

The graph of an exponential function is shown. What is the range of this function represented as an inequality?

• y ≥ 0

• y ≥ 1

• y > 1

• y > 0