Exponential Function Transformations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is a positive real number, and x is the exponent.

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is y = b^x, where b is a positive constant.

Front

What does it mean to reflect a function across the x-axis?

Back

Reflecting a function across the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is a vertical translation in the context of function transformations?

Back

A vertical translation shifts the graph of a function up or down without changing its shape.

Front

What is a horizontal translation in the context of function transformations?

Back

A horizontal translation shifts the graph of a function left or right without changing its shape.

Front

How does the transformation y = a * b^(x - h) + k affect the graph?

Back

This transformation translates the graph horizontally by h units and vertically by k units.

Front

What is the effect of a negative coefficient in front of an exponential function?

Back

A negative coefficient reflects the graph across the x-axis.

Front

What is the range of the function y = b^x?

Back

The range of the function y = b^x is (0, ∞) for b > 0.

Front

What does it mean for a function to be translated right 3 units?

Back

It means that every point on the graph of the function is moved 3 units to the right on the x-axis.

Front

What is the transformation of the function y = 2^(x + 1)?

Back

This function is translated left 1 unit from its parent function y = 2^x.