Question

the graph of g is a translation 3 units up and 1 unit right of the graph of f(x) = \sqrt{x}. which is an equation for g?

a. g(x) = \sqrt{x - 3} + 1
b. g(x) = \sqrt{x - 1} + 3
c. g(x) = \sqrt{x + 3} + 1
d. g(x) = \sqrt{x + 1} + 3

Explanation:

Apply horizontal translation

$$ x \to x - 1 $$

$$ f(x - 1) = \sqrt{x - 1} $$

Apply vertical translation

$$ g(x) = f(x - 1) + 3 $$

$$ g(x) = \sqrt{x - 1} + 3 $$

Answer:

• A. \(g(x) = \sqrt{x - 3} + 1\)
• B. \(g(x) = \sqrt{x - 1} + 3\) (Correct answer)
• C. \(g(x) = \sqrt{x + 3} + 1\)
• D. \(g(x) = \sqrt{x + 1} + 3\)