How do you write and graph a function that translates $y = \sqrt{x}$ $y=sqrtx$ by shifting 5 units right and 3 units up?

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Answer 1 · 2017-06-06T16:51:11

$y = 3 + \sqrt{x - 5}$ $y=3+sqrt(x-5)$

graph{sqrt(x-5) +3 [-10, 10, -5, 5]}

The function $y = \sqrt{x}$ $y=sqrt(x)$ looks like this:

graph{sqrt(x) [-10, 10, -5, 5]}

Shifting the function 5 units to the right means translating the function 5 units along the x-axis. So we will subtract $5$ $5$ from $x$ $x$ .

$y = \sqrt{x - 5}$ $y=sqrt(x-5)$

graph{sqrt(x-5) [-10, 10, -5, 5]}

Add 3 to shift the function 3 units up:

$y = 3 + \sqrt{x - 5}$ $y=3+sqrt(x-5)$

graph{sqrt(x-5) +3 [-10, 10, -5, 5]}

How do you write and graph a function that translates y=√xy=sqrtx by shifting 5 units right and 3 units up?