Question

here are four graphs of functions, f(x), and their horizontally scaled transformations, g(x). describe how to scale a function horizontally.

Explanation:

Step1: Understand the horizontal scaling formula

For a function \(y = f(x)\), if we have \(y = f(kx)\) where \(k>0\).

Step2: Analyze the effect of \(k\)

When \(k > 1\) (in our case \(k = 2\)), the graph of \(y=f(kx)\) is a horizontal compression of the graph of \(y = f(x)\) by a factor of \(\frac{1}{k}\).

Answer:

To horizontally scale a function \(y = f(x)\) to get \(y=f(kx)\) (\(k>0\)): If \(k>1\), the graph of \(y = f(x)\) is compressed horizontally by a factor of \(\frac{1}{k}\). For \(g(x)=f(2x)\) (where \(k = 2\)), the graph of \(f(x)\) is compressed horizontally by a factor of \(\frac{1}{2}\).