Exponential Function Transformations

Front

What is the domain of an exponential function?

Back

The domain of an exponential function is all real numbers.

Front

What is the range of an exponential function that approaches a horizontal asymptote?

Back

The range of an exponential function is typically y > k or y < k, where k is the horizontal asymptote.

Front

What does it mean to shift an exponential function to the right?

Back

Shifting an exponential function to the right means adding a positive value to the x variable in the function.

Front

What does it mean to shift an exponential function to the left?

Back

Shifting an exponential function to the left means subtracting a positive value from the x variable in the function.

Front

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

Back

A vertical stretch occurs when the output of the function is multiplied by a factor greater than 1.

Front

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

Back

A vertical shrink occurs when the output of the function is multiplied by a factor between 0 and 1.

Front

What is a reflection over the x-axis in an exponential function?

Back

A reflection over the x-axis inverts the output values of the function, changing positive values to negative.

Front

How does a horizontal shift affect the graph of an exponential function?

Back

A horizontal shift moves the graph left or right without changing its shape.

Front

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

Back

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

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^(x - h) + k, where (h, k) is the shift.