Question

Which of the following exponential equations shows a horizontal stretch of the function y=7x ?

Answer 1

To achieve a horizontal stretch of an exponential function, you need to modify the input variable \( x \) in such a way that it decreases the rate of growth. For the function \( y = 7^x \), a horizontal stretch can be expressed as \( y = 7^{kx} \), where \( k \) is a constant between 0 and 1.

For example, if you choose \( k = 0.5 \), the equation would become:

\[
y = 7^{0.5x} = 7^{x/2}
\]

This transformation stretches the graph of \( y = 7^x \) horizontally.

In general, for a horizontal stretch, you can use any equation of the form \( y = 7^{kx} \) where \( 0 < k < 1 \).