Question

How is the graph of the parent function of y = 3√x transformed to produce the graph y = 3√1/2x? It is horizontally stretched by a factor of 1/2. It is vertically stretched by a factor of 1/2. It is translated left by 1/2 unit. It is translated right by 1/2 unit.

Answer 1

The graph of the parent function is horizontally stretched by a factor of $\frac{1}{2}$ ⇒ 1st answer

Step-by-step explanation:

Let us revise some transformation

A horizontal compression (or shrinking) is the squeezing of the graph toward the y-axis.  

A horizontal stretching is the stretching of the graph away from the y-axis  

• If k > 1, the graph of y = f(k•x) is the graph of f(x) horizontally shrunk (or compressed) by dividing each of its x-coordinates by k.
• If 0 < k < 1 (a fraction), the graph of y = f(k•x) is the graph of f(x) horizontally stretched by dividing each of its x-coordinates by k
• If k should be negative, the horizontal stretch or shrink is followed by a reflection across the y-axis

A vertical stretching is the stretching of the graph away from the

x-axis  

A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis.  

• If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched by multiplying each of its y-coordinates by 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 multiplying each of its y-coordinates by k
• If k should be negative, the vertical stretch or shrink is followed by a reflection across the x-axis.  

∵  $y=3\sqrt{x}$ is a parent function

∵ Its graph transformed to produce the graph of $y=3\sqrt{\frac{1}{2} x}$

- That means x is multiplied by a factor k, then it is compressed

   or stretched horizontally

∵ k = $\frac{1}{2}$

- The factor $\frac{1}{2}$ is between 0 and 1, then it is

   stretched horizontally as the second rule above

∴ The graph of the parent function is stretched horizontally by a

   factor of $\frac{1}{2}$

The graph of the parent function is horizontally stretched by a factor of $\frac{1}{2}$

Look to the attached figure for more understand

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