Radical Equations and Extraneous Roots Answers

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

Which statements about the graph of the function are true?

Which functions represent exponential growth?

Which shows the domain and range of these functions?

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

If h is instead negative, the curve shifts

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

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

y = 3x

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

Which functions have a horizontal asymptote?

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

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

y = 3−x

The graph of an exponential function has .

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

y = −3x

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.

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

If k is instead negative, the graph shifts

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.

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

Which function represents a vertical stretch of an exponential function?

Which function represents a horizontal compression of an exponential function?