Which form represents a square root function?

Which form represents a square root function?

• A. f(x) = sqrt(ax + b)
• B. f(x) = x^2 + b
• C. f(x) = 1/x
• D. f(x) = log x

Answer: (A)

A square root function has the square-root operation applied to a quantity that changes linearly with x. The parent form is f(x) = sqrt(x); it begins at zero and increases as x grows, with outputs always nonnegative. When you see f(x) = sqrt(ax + b), you’re taking the square root of a linear expression. That fits the square root family: the inside ax + b must be nonnegative (so the domain is ax + b ≥ 0), and the outputs stay nonnegative (the range is y ≥ 0). This is the form that directly represents a square root function, just with horizontal/vertical scaling and shift from the constants a and b. The other options represent different families: a quadratic function x^2 + b is a parabola opening upward; a reciprocal function 1/x forms a hyperbola with asymptotes; a logarithmic function log x is defined for x > 0 and grows differently. None of those are square root functions.

A square root function has the square-root operation applied to a quantity that changes linearly with x. The parent form is f(x) = sqrt(x); it begins at zero and increases as x grows, with outputs always nonnegative.

When you see f(x) = sqrt(ax + b), you’re taking the square root of a linear expression. That fits the square root family: the inside ax + b must be nonnegative (so the domain is ax + b ≥ 0), and the outputs stay nonnegative (the range is y ≥ 0). This is the form that directly represents a square root function, just with horizontal/vertical scaling and shift from the constants a and b.

The other options represent different families: a quadratic function x^2 + b is a parabola opening upward; a reciprocal function 1/x forms a hyperbola with asymptotes; a logarithmic function log x is defined for x > 0 and grows differently. None of those are square root functions.