The equation f(x)=4^x−5

Question

is transformed to 4^2^x−5
. Identify the value of k. Does the graph show a stretch or a compression?(1 point)
Responses

2; compression
2; compression

2; stretch
2; stretch

2x
; stretch
2 x ; stretch

2x
; compression

Answer 1

To transform the function \( f(x) = 4^x - 5 \) to \( f(x) = 4^{2^x} - 5 \), we can observe the exponential term.

1. The original function is \( 4^x \).
2. The transformed function is \( 4^{2^x} \).

This transformation involves replacing \( x \) with \( 2^x \).

This indicates that the function is experiencing a change in its input that is nonlinear. The transformation from using \( x \) to \( 2^x \) suggests that the graph of the function will stretch vertically.

Now, to identify the value of \( k \) in the context, we have:

• The transformation related to \( 2^x \) indicates that the function is stretched because it is growing at a rate that is faster than a linear transformation.

Thus, the answer is:

2; stretch