What is the effect on the graph of f(x) = x2 when it is transformed to h(x) = 2x2 + 15?A.The graph of f(x) is vertically stretched by a factor of 2 and shifted 15 units up.B.The graph of f(x) is vertically stretched by a factor of 2 and shifted 15 units to the left.C.The graph of f(x) is horizontally compressed by a factor of 2 and shifted 15 units to the left.D.The graph of f(x) is horizontally stretched by a factor of 2 and shifted 15 units up.SUBMITarrow_backPREVIOUS
Question
What is the effect on the graph of f(x) = x2 when it is transformed to h(x) = 2x2 + 15?A.The graph of f(x) is vertically stretched by a factor of 2 and shifted 15 units up.B.The graph of f(x) is vertically stretched by a factor of 2 and shifted 15 units to the left.C.The graph of f(x) is horizontally compressed by a factor of 2 and shifted 15 units to the left.D.The graph of f(x) is horizontally stretched by a factor of 2 and shifted 15 units up.SUBMITarrow_backPREVIOUS
Solution
The correct answer is A. The graph of f(x) = x^2 is vertically stretched by a factor of 2 and shifted 15 units up when it is transformed to h(x) = 2x^2 + 15.
Here's why:
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The coefficient of x^2 in h(x) is 2, which is a vertical stretch by a factor of 2. This means that every y-coordinate in the original graph, f(x), is multiplied by 2 in the new graph, h(x).
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The constant term in h(x) is +15, which is a vertical shift upwards by 15 units. This means that every point on the graph of f(x) is moved 15 units up to form the graph of h(x).
The other options involve horizontal shifts or stretches/compressions, but the equation h(x) = 2x^2 + 15 does not involve any changes to the x-coordinates, so these options are incorrect.
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