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 translate a function?

Back

Translating a function means shifting its graph horizontally or vertically without changing its shape.

Front

What is a vertical translation?

Back

A vertical translation moves the graph of a function up or down. For example, f(x) + k translates the graph up by k units if k > 0, and down if k < 0.

Front

What is a horizontal translation?

Back

A horizontal translation moves the graph of a function left or right. For example, f(x - h) translates the graph right by h units if h > 0, and left if h < 0.

Front

What is a reflection in the context of functions?

Back

A reflection is a transformation that flips the graph of a function over a specified line, such as the x-axis or y-axis.

Front

How do you reflect a function over the x-axis?

Back

To reflect a function over the x-axis, you multiply the function by -1. For example, f(x) becomes -f(x).

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 over the x-axis.

Front

What does it mean to stretch a function?

Back

Stretching a function means to increase or decrease its steepness. A vertical stretch occurs when the function is multiplied by a factor greater than 1.

Front

What is the transformation of f(x) = 2^x when it becomes f(x) = 2^(x - 3)?

Back

The transformation is a horizontal translation to the right by 3 units.