What is the equation of the graph that represents the parent function f(x) = x4 stretched vertically by a factor of 2, and then shifted up 3 spaces.A.g(x) = 2(x + 3)4B.g(x) = 2x4 - 3C.g(x) = 2x4 + 3D.g(x) = 2(x4 + 3)SUBMITarrow_backPREVIOUS
Question
What is the equation of the graph that represents the parent function f(x) = x4 stretched vertically by a factor of 2, and then shifted up 3 spaces.A.g(x) = 2(x + 3)4B.g(x) = 2x4 - 3C.g(x) = 2x4 + 3D.g(x) = 2(x4 + 3)SUBMITarrow_backPREVIOUS
Solution
The correct answer is C. g(x) = 2x^4 + 3.
Here's why:
Step 1: The parent function f(x) = x^4 is given.
Step 2: When it is stretched vertically by a factor of 2, the function becomes f(x) = 2x^4. This is because the vertical stretch is achieved by multiplying the output of the function by the stretch factor.
Step 3: Then, the function is shifted up 3 spaces. This is achieved by adding 3 to the function. So, the final function becomes g(x) = 2x^4 + 3.
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