Exponential Transformations

Front

What is a horizontal translation in exponential functions?

Back

A horizontal translation shifts the graph of the function left or right along the x-axis. For example, g(x) = f(x - h) translates the graph of f(x) to the right by h units.

Front

What does it mean to reflect a function across the horizontal asymptote (HA)?

Back

Reflecting a function across the horizontal asymptote means flipping the graph over the line that represents the horizontal asymptote, changing the direction of the function's growth.

Front

How do you represent a vertical translation of a function?

Back

A vertical translation shifts the graph of the function up or down. For example, g(x) = f(x) + k translates the graph of f(x) up by k units if k is positive and down if k is negative.

Front

What is the effect of the transformation g(x) = f(x + 2)?

Back

This represents a horizontal translation of the function f(x) to the left by 2 units.

Front

What is the transformation for g(x) = -f(x)?

Back

This represents a reflection of the function f(x) across the x-axis.

Front

If g(x) = f(x) - 4, what transformation occurs?

Back

This represents a vertical translation of the function f(x) down by 4 units.

Front

What does the transformation g(x) = f(x - 1) + 3 indicate?

Back

This indicates a horizontal translation of the function f(x) to the right by 1 unit and a vertical translation up by 3 units.

Front

What is the transformation for g(x) = 2^(-x)?

Back

This represents a reflection of the function 2^x across the y-axis.

Front

How do you determine the transformations applied to f(x) = 2^x to get g(x) = -2^(x + 3) - 6?

Back

The transformations are: reflection across the x-axis, horizontal translation left by 3 units, and vertical translation down by 6 units.

Front

What is the transformation for g(x) = 2^(x - 3)?

Back

This represents a horizontal translation of the function 2^x to the right by 3 units.