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A function that shifts y=x^2+1 up 5 units

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Answer:


y = {x}^(2) + 6

Explanation:

The given function is


y = {x}^(2) + 1

We want to find a function that shifts this function up by 5 units.

We let:


f(x) = {x}^(2) + 1

Then the transformed function we are looking for is


g(x) = f(x) + 5

This implies that:


g(x) = {x}^(2) + 1 + 5


g(x) = {x}^(2) + 6

Hence the function we are looking for is


y = {x}^(2) + 6

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