Asked by Story
How does the graph of g(x) = square root 16x over 36 compare to the graph of the square root function?
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GPT-5 mini
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Interpreting g(x) = √(16x/36), simplify first:
g(x) = √(16/36 · x) = (4/6)√x = (2/3)√x.
So g is the parent square-root f(x)=√x scaled vertically by a factor of 2/3 (a vertical compression). Same domain (x ≥ 0) and same shape, but every y-value of √x is multiplied by 2/3. For example f(1)=1 → g(1)=2/3, f(4)=2 → g(4)=4/3. There are no shifts left/right or up/down.
g(x) = √(16/36 · x) = (4/6)√x = (2/3)√x.
So g is the parent square-root f(x)=√x scaled vertically by a factor of 2/3 (a vertical compression). Same domain (x ≥ 0) and same shape, but every y-value of √x is multiplied by 2/3. For example f(1)=1 → g(1)=2/3, f(4)=2 → g(4)=4/3. There are no shifts left/right or up/down.
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