Question

which function is graphed?

a. (f(x) = \sqrt3{x + 4} + 1)
b. (f(x) = \sqrt3{x + 1} + 4)
c. (f(x) = \sqrt3{x - 4} + 1)
d. (f(x) = \sqrt3{x + 1} - 4)

Explanation:

Identify the inflection point of the cube root function

$$ (h, k) = (4, 1) $$

Apply the transformation formula

$$ f(x) = \sqrt[3]{x - h} + k \implies f(x) = \sqrt[3]{x - 4} + 1 $$

Verify with a point on the graph

$$ f(5) = \sqrt[3]{5 - 4} + 1 = 1 + 1 = 2 $$

Answer:

• A. \(f(x) = \sqrt[3]{x + 4} + 1\)
• B. \(f(x) = \sqrt[3]{x + 1} + 4\)
• C. \(f(x) = \sqrt[3]{x - 4} + 1\) (Correct answer)
• D. \(f(x) = \sqrt[3]{x + 1} - 4\)