Graphing Exponential Functions Answers

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

The graph of an exponential function has .

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 statements about the graph of the function are true?

Which functions represent exponential growth?

Which functions have a horizontal asymptote?

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

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 .

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

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

y = 3x

Identify the horizontal asymptote of each graph.

The domain of the function is to because an exponent can be any real number.

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

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

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

y = 3−x

The domain of the function is to because an exponent can be any real number.

Question text not available

Which statements are true about the graph?

y = −3x

The range of the function is to because 4x is always positive.

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

The range of the function is to because 4x is always positive.

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?