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 does it mean to translate a function?

Back

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

Front

What is the parent function of exponential functions?

Back

The parent function of exponential functions is f(x) = b^x, where b > 0.

Front

What transformation occurs when a function is written as f(x) = b^(x-h)?

Back

The graph is translated horizontally to the right by 'h' units if h > 0, and to the left if h < 0.

Front

What transformation occurs when a function is written as f(x) = b^x + k?

Back

The graph is translated vertically upward by 'k' units if k > 0, and downward if k < 0.

Front

What does it mean for a function to be reflected over the x-axis?

Back

A reflection over the x-axis means that the output values (y-values) of the function are multiplied by -1.

Front

How do you reflect an exponential function over the line x=0?

Back

To reflect an exponential function over the line x=0, replace x with -x in the function.

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 is the range of the function f(x) = 2^x?

Back

The range of f(x) = 2^x is (0, ∞), meaning y is greater than 0.

Front

What does it mean for a function to be stretched?

Back

A function is stretched vertically if the output values are multiplied by a factor greater than 1.