Exponential Function Transformations

What is the general form of an exponential function?

• y = a * b^x

• y = a + b^x

• y = a / b^x

• y = a * b * x

Tags

CCSS.HSF.LE.A.2

How does the value of 'a' in the function y = a^x affect the graph?

• The value of 'a' has no effect on the graph

• The value of 'a' determines the x-intercept of the graph

• The value of 'a' changes the color of the graph

• The value of 'a' in the function y = a^x affects the steepness of the graph.

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.LE.B.5

Explain how the function y = 2^x differs from y = 3^x in terms of their graphs.

• The graphs of y = 2^x and y = 3^x differ in their concavity.

• The graphs of y = 2^x and y = 3^x differ in their rate of growth.

• The graphs of y = 2^x and y = 3^x differ in their domain and range.

• The graphs of y = 2^x and y = 3^x differ in their y-intercept.

Tags

CCSS.HSF-IF.C.7E

What is the effect of the value of 'b' in the function y = 2^(bx) on the graph?

• Change in y-intercept

• Vertical stretch or compression

• Change in slope

• Horizontal shift

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.LE.B.5

Describe the transformation when the function y = 2^x is changed to y = 2^(x+3).

• Shifted 3 units to the left

• No transformation applied

• Reflected over the x-axis

• Shifted 3 units to the right

Tags

CCSS.HSF.BF.B.3

How does the function y = 2^x differ from y = 2^(x-4) in terms of their graphs?

• They differ by a vertical shift upwards by 4 units.

• They differ by a horizontal shift to the right by 4 units.

• They differ by a horizontal shift to the left by 4 units.

• They differ by a vertical shift downwards by 4 units.

Tags

CCSS.HSF.BF.B.3

Explain the transformation when the function y = 2^x is changed to y = 3*2^x.

• Dividing the original function y = 2^x by 3

• Subtracting 3 from the original function y = 2^x

• Adding 3 to the original function y = 2^x

• Multiplying the original function y = 2^x by 3

Tags

CCSS.HSF.BF.B.3

What is the impact of the value of 'c' in the function y = 2^(x+c) on the graph?

• It shifts the graph vertically

• It shifts the graph horizontally

• It has no impact on the graph

• It stretches the graph vertically

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.LE.B.5

Describe the transformation when the function y = 2^x is changed to y = 2^(x-2)+3.

• Shifted 3 units to the left and 2 units down

• Shifted 2 units to the right and 2 units down

• Shifted 2 units to the left and 3 units down

• Shifted 2 units to the right and 3 units up

Tags

CCSS.HSF.BF.B.3

How does the function y = 2^x differ from y = 2^(x/2) in terms of their graphs.

• The graphs differ in that y = 2^(x/2) is a vertically compressed version of y = 2^x.

• The graphs differ in that y = 2^(x/2) is a reflection of y = 2^x over the x-axis.

• The graphs differ in that y = 2^(x/2) is a horizontally compressed version of y = 2^x.

• The graphs differ in that y = 2^(x/2) is a steeper version of y = 2^x.

Tags

CCSS.HSF-IF.C.7E