AP PreCalc / Exponential Function Transformations

Assume all parent functions are y = 2^x.

Describe the transformation: y = 2^x + 3

Shift up 3.

Describe the transformation: y = 2^x - 3

Shift down 3.

Describe the transformation: y = 2^x-3

Shift right 3.

Describe the transformation: y = 2^x+3

Shift left 3.

Describe the transformation: y = 4 * 2^x

Vertical stretch 4.

Describe the transformation: y = 1/4 * 2^x

Vertical shrink 1/4.

Describe the transformation: y = 2^1/₄x

Horizontal stretch 4.

Describe the transformation: y = 2^4x

Horizontal shrink 1/4.

Describe the transformation: y = -2^x

Reflect over x-axis.

Describe the transformation: y = 2^-x

Reflect over y-axis.