Answer:
The graph of g(x) is the graph of f(x) stretched horizontally by a factor of 4 ⇒ 3rd answer
Step-by-step explanation:
Let us revise the vertical and horizontal stretch
Vertical stretch/compressed
- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by a factor k
- If 0 < k < 1 (a fraction), the graph of y = k•f(x) is the graph of f(x) vertically shrunk (or compressed) by a factor k
Horizontal stretch/compressed
- If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally shrunk (or compressed) by a factor [tex]\frac{1}{k}[/tex]
- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is the graph of f(x) horizontally stretched by a factor [tex]\frac{1}{k}[/tex]
∵ g(x) = f([tex]\frac{1}{4}[/tex] x)
∵ [tex]f(x)=\sqrt{x}[/tex]
∴ [tex]g(x)=\sqrt{\frac{1}{4}x}[/tex]
- That means x is multiplied by [tex]\frac{1}{4}[/tex]
∵ 0 < [tex]\frac{1}{4}[/tex] < 1
∴ k = [tex]\frac{1}{4}[/tex]
∵ The factor = [tex]\frac{1}{k}[/tex]
∵ [tex]\frac{1}{\frac{1}{4}}=4[/tex]
∴ The factor = 4
∴ The graph of g(x) is the graph of f(x) stretched horizontally
by a factor of 4
Look to the attached graph for more understand
