The graph of y=√x is translated 5 units to the left and 7 units up. What is the equation of the graph that results from this translation?

Answer: sqrt(x+5)+7.

If you have a function y=f(x-h)+k, where f is a base function, h is a horizontal translation, and k is a vertical translation:

To shift 5 units to the left and 7 units up, h must be -5, and k must be 7. So the equation is f(x+7)+k=sqrt(x+5) + 7.

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jimrgrant1 jimrgrant1 · Answer 2 · 2020-08-09T19:37:36+02:00

Answer:

y = [tex]\sqrt{x+5}[/tex] + 7

Step-by-step explanation:

Given the graph of f(x) then f(x + k) is a horizontal translation of f(x)

• If k > 0 then a shift to the left of k units

• If k < 0 then a shift to the right of k units

Thus a translation of 5 units to the left

y = [tex]\sqrt{x+5}[/tex]

Given the graph of f(x) then f(x) + c is a vertical translation of f(x)

• If c > 0 then shift up by c units

• If c < 0 then shift down by c units

Thus

y = [tex]\sqrt{x+5}[/tex] + 7 ← translated equation