Question

If f left-parenthesis x right-parenthesis equals x squared minus 1, which of the following ordered pairs are on the graph of f left-parenthesis x right-parenthesis? Select all that apply.
(2 points)
Responses

left-parenthesis 0 comma 1 right-parenthesis
Image with alt text: left-parenthesis 0 comma 1 right-parenthesis

left-parenthesis 1 comma 0 right-parenthesis
Image with alt text: left-parenthesis 1 comma 0 right-parenthesis

left-parenthesis 3 comma 5 right-parenthesis
Image with alt text: left-parenthesis 3 comma 5 right-parenthesis

left-parenthesis 5 comma 24 right-parenthesis
Image with alt text: left-parenthesis 5 comma 24 right-parenthesis

left-parenthesis negative 2 comma 3 right-parenthesis
Image with alt text: left-parenthesis negative 2 comma 3 right-parenthesis

left-parenthesis negative 4 comma negative 17 right-parenthesis

Answer 1

To determine if an ordered pair is on the graph of f(x), we substitute the x-coordinate of the ordered pair into the function and check if the resulting y-coordinate is equal to the given y-coordinate.

For f(x) = x^2 - 1,

Substituting x = 0, we get f(0) = 0^2 - 1 = -1. So, (0, 1) is not on the graph of f(x).

Substituting x = 1, we get f(1) = 1^2 - 1 = 0. So, (1, 0) is on the graph of f(x).

Substituting x = 3, we get f(3) = 3^2 - 1 = 8. So, (3, 5) is not on the graph of f(x).

Substituting x = 5, we get f(5) = 5^2 - 1 = 24. So, (5, 24) is on the graph of f(x).

Substituting x = -2, we get f(-2) = (-2)^2 - 1 = 3. So, (-2, 3) is not on the graph of f(x).

Substituting x = -4, we get f(-4) = (-4)^2 - 1 = 15. So, (-4, -17) is not on the graph of f(x).

Therefore, the ordered pairs (1, 0) and (5, 24) are on the graph of f(x).