Questions: Given f(x) (black graph) sketch a graph defined by g(x)=2 * f(x)

Transcript text: Given $\mathrm{f}(\mathrm{x})$ (black graph) sketch a graph defined by \[ \mathrm{g}(\mathrm{x})=2 \cdot \mathrm{f}(\mathrm{x}) \]

Solution

Step 1: Identify the vertex of f(x)

The vertex of the black parabola f(x) is at (1,2).

Step 2: Identify another point on f(x)

Another point on the graph of f(x) is (0,4).

Step 3: Transform the vertex of f(x) to find the vertex of g(x)

Since g(x) = 2 * f(x), we multiply the y-coordinate of the vertex of f(x) by 2. The vertex of g(x) becomes (1, 2*2) = (1,4).

Step 4: Transform the other point on f(x) to find a point on g(x)

Multiply the y-coordinate of the point (0,4) on f(x) by 2 to find the corresponding point on g(x). The point becomes (0, 4*2) = (0,8).

The orange parabola represents g(x). It has a vertex at (1,4) and passes through the point (0,8). It is a vertically stretched version of f(x).

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