Exponential Function Transformations

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (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 f(x) = b^x, where b > 0 and b ≠ 1.

Front

What does it mean to reflect a function over the line x=0?

Back

Reflecting a function over the line x=0 means to replace x with -x in the function's equation.

Front

How do you translate a function 4 units to the right?

Back

To translate a function 4 units to the right, replace x with (x - 4) in the function's equation.

Front

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

Back

A negative sign in front of an exponential function reflects the graph across the x-axis.

Front

What is a vertical translation in the context of exponential functions?

Back

A vertical translation moves the graph up or down. For example, f(x) = b^x + k translates the graph k units vertically.

Front

What is the range of the function f(x) = b^x?

Back

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

Front

What does it mean to translate a function left or right?

Back

Translating a function left or right involves shifting the graph horizontally. Left is achieved by adding to x, and right by subtracting from x.

Front

What is the transformation of the function f(x) = -2^(x - 3)?

Back

The transformation is a reflection across the x-axis and a translation right 3 units.

Front

How do you identify the parent function from a transformed function?

Back

To identify the parent function, look for the base form of the function without transformations such as shifts or reflections.