Question

use the graph of y = f(x) to graph the function g.
g(x) = f(2x)

choose the correct graph below.
○ a.
○ b.
○ c.
○ d.

Explanation:

Step1: Horizontal compression rule

For a function \(y = f(x)\), the graph of \(y = f(kx)\) (\(k>1\)) is a horizontal compression of the graph of \(y = f(x)\) by a factor of \(\frac{1}{k}\). Here \(k = 2\), so the graph of \(y=f(2x)\) is a horizontal compression of \(y = f(x)\) by a factor of \(\frac{1}{2}\).

Step2: Analyzing key - points

Let's assume some key - points on \(y = f(x)\). If we have a point \((x,y)\) on \(y=f(x)\), then the corresponding point on \(y = f(2x)\) is \((\frac{x}{2},y)\). For example, if \((x_0,y_0)\) is on \(y = f(x)\), when we consider \(g(x)=f(2x)\), setting \(2x=x_0\) gives \(x=\frac{x_0}{2}\) and \(y = y_0\).

Answer:

C.