Exponential Function Transformations

Front

What is the range of an exponential function of the form y = a^x where a > 0?

Back

y > 0

Front

What transformation occurs when the function y = a^(x-h) is applied?

Back

The graph is translated h units to the right.

Front

What transformation occurs when the function y = a^(x) + k is applied?

Back

The graph is translated k units up.

Front

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

Back

The output values (y-values) are multiplied by -1.

Front

What is the parent function of exponential functions?

Back

y = a^x, where a > 0.

Front

If y = 2^(x-3), what transformation is applied to the parent function y = 2^x?

Back

Translated right 3 units.

Front

If y = -3^(x+2), what transformations are applied to the parent function y = 3^x?

Back

Reflected over the x-axis and translated left 2 units.

Front

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

Back

It reflects the graph over the x-axis.

Front

How do you determine the vertical asymptote of an exponential function?

Back

The vertical asymptote is typically y = 0 for functions of the form y = a^x.

Front

What transformation occurs when the function y = a^x + k is applied?

Back

The graph is translated k units up if k > 0, or down if k < 0.