Question

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

Answer 1

To achieve a horizontal stretch of an exponential function like \( y = 7^x \), we use the transformation involving a horizontal scaling factor. This is typically done by manipulating the exponent of the function.

If \( y = 7^x \) is our original function, to stretch it horizontally, we replace \( x \) with \( \frac{x}{k} \), where \( k > 1 \) is the factor by which we are stretching the graph. Thus, the transformed function would be:

\[
y = 7^{\frac{x}{k}}
\]

For example, if \( k = 2 \), the function representing a horizontal stretch by a factor of 2 would be:

\[
y = 7^{\frac{x}{2}}
\]

So, in general, look for equations of the form \( y = 7^{\frac{x}{k}} \) (with \( k > 1 \)) to indicate a horizontal stretch of the function \( y = 7^x \).