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
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).
To determine which of the ordered pairs are on the graph of f(x) = x^2 - 1, we need to substitute the x-value of each ordered pair into the function and check if the result matches the corresponding y-value.
Let's check each ordered pair one by one:
1) (0, 1)
Substituting x = 0 into the function:
f(0) = (0^2) - 1 = 0 - 1 = -1
The y-value for this ordered pair is not 1, so it is not on the graph.
2) (1, 0)
Substituting x = 1 into the function:
f(1) = (1^2) - 1 = 1 - 1 = 0
The y-value for this ordered pair is 0, so it is on the graph.
3) (3, 5)
Substituting x = 3 into the function:
f(3) = (3^2) - 1 = 9 - 1 = 8
The y-value for this ordered pair is not 5, so it is not on the graph.
4) (5, 24)
Substituting x = 5 into the function:
f(5) = (5^2) - 1 = 25 - 1 = 24
The y-value for this ordered pair is 24, so it is on the graph.
5) (-2, 3)
Substituting x = -2 into the function:
f(-2) = (-2^2) - 1 = 4 - 1 = 3
The y-value for this ordered pair is 3, so it is on the graph.
6) (-4, -17)
Substituting x = -4 into the function:
f(-4) = (-4^2) - 1 = 16 - 1 = 15
The y-value for this ordered pair is not -17, so it is not on the graph.
Therefore, the ordered pairs that are on the graph of f(x) = x^2 - 1 are:
(1, 0)
(5, 24)
(-2, 3)