Question

given the function f(x) = 2x + 1, describe the transformation from f(x) to g(x) if g(x) = 0.2f(x).
the function f(x) is compressed vertically
the function f(x) is stretched vertically
the function f(x) is compressed horizontally
the function f(x) is stretched horizontally

Explanation:

Step1: Recall vertical transformation rule

For a function \(y = af(x)\), if \(0 < a< 1\), the graph of \(y = f(x)\) is vertically compressed by a factor of \(a\). If \(a>1\), the graph of \(y = f(x)\) is vertically stretched by a factor of \(a\).

Step2: Analyze the given transformation

Here, \(g(x)=0.2f(x)\) where \(a = 0.2\) and \(0<0.2<1\).

Answer:

The function \(f(x)\) is compressed vertically.