Understanding Graph Transformations of Exponential Functions

The video tutorial explains how to match graphs to their corresponding functions by analyzing transformations of the function f(x) = e^x. It covers reflections across the Y axis, X axis, and both axes, demonstrating how these transformations affect the graph's appearance. The tutorial uses specific examples to illustrate each type of reflection and the resulting graph, helping viewers understand the impact of changing signs in the function's equation.

What is the basic function that the graphs are being compared to?

• f(x) = e^x

• f(x) = x^2

• f(x) = ln(x)

• f(x) = sin(x)

Tags

CCSS.HSF.BF.B.3

What transformation does the function y = e^-x represent?

• Reflection across the x-axis

• Reflection across the y-axis

• Translation upwards

• Translation downwards

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CCSS.HSF-IF.C.7E

Which graph corresponds to the function y = e^-x?

• Graph A

• Graph B

• Graph D

• Graph C

Tags

CCSS.HSF.BF.B.3

What happens to the y-values in the transformation y = -e^x?

• They remain unchanged

• They become positive

• They become negative

• They double

Tags

CCSS.HSF-IF.C.7E

Which graph corresponds to the function y = -e^x?

• Graph B

• Graph C

• Graph A

• Graph D

Tags

CCSS.HSF.BF.B.3

What transformation does the function y = -e^-x represent?

• No reflection

• Reflection across both axes

• Reflection across the x-axis

• Reflection across the y-axis

Tags

CCSS.HSF-IF.C.7E

Which graph corresponds to the function y = -e^-x?

• Graph D

• Graph B

• Graph A

• Graph C

Tags

CCSS.HSF.BF.B.3

What is the effect of changing the sign of the x-values in a function?

• Translation to the right

• Reflection across the x-axis

• Translation to the left

• Reflection across the y-axis

Tags

CCSS.HSF.BF.B.3

What is the effect of changing the sign of the y-values in a function?

• Translation downwards

• Translation upwards

• Reflection across the y-axis

• Reflection across the x-axis

What is the combined effect of changing the signs of both x and y values in a function?

• Reflection across both axes

• No change

• Reflection across the x-axis

• Reflection across the y-axis