Problem

If $(-3,1)$ is a point on the graph of $y=f(x)$, which of the following must be on the graph of $y=8 f(x)$ ?
Choose the correct answer below.
$(-3,1)$
$(-24,1)$
$(-24,8)$
$(-3,8)$

Answer

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Answer

Final Answer: The point that must be on the graph of \(y=8f(x)\) is \(\boxed{(-3,8)}\).

Steps

Step 1 :The function \(y=f(x)\) is being scaled by a factor of 8 to get \(y=8f(x)\). This means that the y-coordinate of any point on the graph of \(y=f(x)\) will be multiplied by 8 to get the corresponding point on the graph of \(y=8f(x)\).

Step 2 :Therefore, the point \((-3,1)\) on the graph of \(y=f(x)\) will correspond to the point \((-3,8)\) on the graph of \(y=8f(x)\).

Step 3 :Final Answer: The point that must be on the graph of \(y=8f(x)\) is \(\boxed{(-3,8)}\).

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