Questions: The graph of (y=f(x)) is shown below. Draw the graph of (y=frac12 f(x)).

$The graph of (y=f(x)) is shown below. Draw the graph of (y=frac12 f(x)).$

Transcript text: The graph of $y=f(x)$ is shown below. Draw the graph of $y=\frac{1}{2} f(x)$. I Don't Know Submit

Solution

Solution Steps

Step 1: Identify two points on the original line.

Two points on the given line are (-2, 2) and (2, 4).

Step 2: Determine the transformation.

Multiplying the function by $\frac{1}{2}$ results in a vertical compression by a factor of $\frac{1}{2}$. This means the y-coordinates of each point on the original graph will be multiplied by $\frac{1}{2}$.

Step 3: Apply the transformation to the chosen points.

Applying the transformation to the point (-2, 2) gives us (-2, 1). Applying it to (2, 4) gives (2, 2).

Step 4: Plot the transformed points and draw the new line.

Plot the points (-2, 1) and (2, 2) on the graph. Draw a straight line through these points. This is the graph of $y = \frac{1}{2}f(x)$.

Final Answer

The graph of $y = \frac{1}{2}f(x)$ is the line passing through the points (-2, 1) and (2, 2).

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