Graphing Exponential Functions Answers

Which functions represent exponential growth?

The parent function y = 0.5x is across its domain because its base, b, is such that .

y = 3x

The domain of an exponential function is . The range of an exponential function is .

Which statements about the graph of the function are true?

Explore transformations of the basic exponential function , shown right. First, change the slider for h to positive values such as 1, 2, or 3. The curve shifts h units

Which functions have a horizontal asymptote?

The parent function y = 0.5x is across its domain because its base, b, is such that .

y = 3−x

The domain of an exponential function is . The range of an exponential function is .

If h is instead negative, the curve shifts

The function, f, shifts the parent function 8 units .

y = −3x

Which shows the domain and range of these functions?

The graph of an exponential function has .

Next, change the slider for k to different positive values. The curve shifts k units

When b > 1, as x grows in the negative direction, y . When 0 < b < 1, as x grows in the negative direction, y .

The function, f, shifts the parent function 5 units .

The graph is throughout its domain and has at the x–axis because the value bx can get very close to 0 but never reach it.

If k is instead negative, the graph shifts

When b > 1, as x grows in the negative direction, y . When 0 < b < 1, as x grows in the negative direction, y .

The graph is throughout its domain and has at the x–axis because the value bx can get very close to 0 but never reach it.

Which function represents a vertical stretch of an exponential function?

Which function represents a horizontal compression of an exponential function?