The graph of the parent function is horizontally stretched by a factor of [tex]\frac{1}{2}[/tex] ⇒ 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. Â
A horizontal stretching is the stretching of the graph away from the y-axis Â
- 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 Â
A vertical compression (or shrinking) is the squeezing of the graph toward the x-axis. Â
- 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. Â
∵  [tex]y=3\sqrt{x}[/tex] is a parent function
∵ Its graph transformed to produce the graph of [tex]y=3\sqrt{\frac{1}{2} x}[/tex]
- That means x is multiplied by a factor k, then it is compressed
  or stretched horizontally
∵ k = [tex]\frac{1}{2}[/tex]
- The factor [tex]\frac{1}{2}[/tex] 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 [tex]\frac{1}{2}[/tex]
The graph of the parent function is horizontally stretched by a factor of [tex]\frac{1}{2}[/tex]
Look to the attached figure for more understand
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