Questions: Use the graph of y=f(x) to sketch the graph of y=2 f(x). Determine the four points on the new graph. The point (-10,0) shifts to which point on the new graph? (Type an ordered pair.) The point (-5,5) shifts to which point on the new graph? (Type an ordered pair.) The point (0,0) shifts to which point on the new graph? (Type an ordered pair.) The point (5,5) shifts to which point on the new graph? (Type an ordered pair.) Choose the best sketch for y=2 f(x). A. B.

Solution Steps

The transformation given is \( y = 2f(x) \). This means that the y-values of the original function \( f(x) \) are multiplied by 2. Therefore, for any point \((x, y)\) on the original graph, the new point on the transformed graph will be \((x, 2y)\).

We will apply the transformation \( y = 2f(x) \) to each of the given points.

Original point: \((-10, 0)\) Transformed point: \((-10, 2 \cdot 0) = (-10, 0)\)

Original point: \((-5, 5)\) Transformed point: \((-5, 2 \cdot 5) = (-5, 10)\)

Original point: \((0, 0)\) Transformed point: \((0, 2 \cdot 0) = (0, 0)\)

We will verify the transformation for the given points and ensure they match the expected results.

Original point: \((5, 5)\) Transformed point: \((5, 2 \cdot 5) = (5, 10)\)

Final Answer