Question

For each exponential function, a) write a new function, and b) sketch the corresponding graph (on the same coordinate plane) based on the description of the transformation.

Answer 1

A reflection over the y-axis means that "x" will change signs.

A dilation causes the graph to stretch (if the factor is greater than 1) or shrink/compress (if the factor is between 0 and 1). Usually, the instructions will say whether it is a vertical or horizontal stretch (or shrink) so you know which variable is affected. Since it was not specified, I am going to assume that this is both a vertical and a horizontal shrink.

Answer: y =
`(1)/(2)`(
`4^(-2x)`)