The transformations that produce g(x)=2^3x -4 from f(x)=2^x are:

Question

A dilation by a factor of (answer) with respect to the (answer). A translation of (answer) units(answer).

Answer 1

The transformations that produce g(x)=2^3x -4 from f(x)=2^x are:

The dilation -- stretching of the graph -- is produced by the change from 2^x to 2^3x. The dilation is by a factor of 2^3x / 2^x = (2^x • 2^x • 2^x) / 2^x = 2^2x. The question asked for "A dilation by a factor of (answer) with respect to the (answer)", but I don't know what "with respect to the (answer)" is supposed to mean.

The translation is produced by the -4, so it's a translation of -4. There are no units here: we're not talking about feet or seconds or kilograms or any other units.