Function Algebra Question

Question

A student graphs the function f(x) = 2(4)^x using a graphing calculator. The student then replaces the 2 in the equation with an 8. Which best describes the change the student sees when graphing the new function?

O The graph of the new function will be vertically shifted up 4 units when compared to the previously graphed function.

O The graph of the new function will be vertically shifted up 6 units when compared to the previously graphed function.

O The graph of the new function will be vertically stretched by a factor of 4 when compared to the previously graphed function.

O The graph of the new function will be vertically stretched by a factor of 6 when compared to the previously graphed function.

Answer 1

1st choice: a shift to the right by 4 would transform 2(4^x) to 2(4^(x-4))

2nd choice a shift vertically up by 6 would transform to 2(4^x)+6

3rd choice a shift vertically by factor of 4 would transform to 8(4^x) which is the only correct answer

4th choice a shift vertically by a factor of 6 would transform to 12(4^x)