Question

Which relation is a function?

A) f(x) = x^2
B) g(x) = ± √x
C) h(x) = sin(x)
D) i(x) = |x|
E) j(x) = 2x + 3

Answer 1

Option A) f(x) = x^2, option C) h(x) = sin(x), option D) i(x) = |x|, and option E) j(x) = 2x + 3 are functions, as each input x has a unique output y. Option B) is not a function because it assigns two outputs to a single input.

Step-by-step explanation:

The question you have asked focuses on identifying which relation is a function. A function, by definition in mathematics, is a relation where each input has exactly one output. Reviewing the options provided:

• A) f(x) = x^2 is a quadratic function where each x value has one corresponding y value.
• B) g(x) = ± √ x is not a function because for each positive x value, there are two possible y values (one positive and one negative).
• C) h(x) = sin(x) is a trigonometric function with one output for each x value, making it a function.
• D) i(x) = |x| is the absolute value function and gives one result for each x value.
• E) j(x) = 2x + 3 is a linear function with a unique y for every x value.

Based on this, the relations that are functions are A), C), D), and E).