Which of the following sets of ordered pairs could represent a function? Select all that apply.
left-brace left-parenthesis 2 comma negative 5 right-parenthesis, left-parenthesis 4 comma negative 5 right-parenthesis, left-parenthesis 6 comma 2 right-parenthesis, left-parenthesis 8 comma 3 right-parenthesis right-braceImage with alt text: left-brace left-parenthesis 2 comma negative 5 right-parenthesis, left-parenthesis 4 comma negative 5 right-parenthesis, left-parenthesis 6 comma 2 right-parenthesis, left-parenthesis 8 comma 3 right-parenthesis right-brace
left-brace left-parenthesis negative 1 comma 5 right-parenthesis, left-parenthesis 3 comma 5 right-parenthesis, left-parenthesis 6 comma 5 right-parenthesis, left-parenthesis 9 comma 5 right-parenthesis right-brace
Image with alt text: left-brace left-parenthesis negative 1 comma 5 right-parenthesis, left-parenthesis 3 comma 5 right-parenthesis, left-parenthesis 6 comma 5 right-parenthesis, left-parenthesis 9 comma 5 right-parenthesis right-brace
left-brace left-parenthesis 3 comma negative 4 right-parenthesis, left-parenthesis 5 comma 2 right-parenthesis, left-parenthesis 3 comma 8 right-parenthesis, left-parenthesis 6 comma 7 right-parenthesis right-brace
Image with alt text: left-brace left-parenthesis 3 comma negative 4 right-parenthesis, left-parenthesis 5 comma 2 right-parenthesis, left-parenthesis 3 comma 8 right-parenthesis, left-parenthesis 6 comma 7 right-parenthesis right-brace
left-brace left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 4 comma 2 right-parenthesis, left-parenthesis negative 1 comma 7 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis right-brace
Image with alt text: left-brace left-parenthesis 0 comma 3 right-parenthesis, left-parenthesis 4 comma 2 right-parenthesis, left-parenthesis negative 1 comma 7 right-parenthesis, left-parenthesis 0 comma 3 right-parenthesis right-brace
left-brace left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis negative 1 comma 6 right-parenthesis, left-parenthesis negative 1 comma 8 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis right-brace
Image with alt text: left-brace left-parenthesis negative 1 comma 1 right-parenthesis, left-parenthesis negative 1 comma 6 right-parenthesis, left-parenthesis negative 1 comma 8 right-parenthesis, left-parenthesis negative 1 comma 0 right-parenthesis right-brace
left-brace left-parenthesis negative 4 comma 2 right-parenthesis, left-parenthesis 3 comma negative 2 right-parenthesis, left-parenthesis negative 4 comma negative 2 right-parenthesis, left-parenthesis 5 comma 1 right-parenthesis right-brace
The sets of ordered pairs that could represent a function are:
1. {(2, -5), (4, -5), (6, 2), (8, 3)}
2. {(-1, 5), (3, 5), (6, 5), (9, 5)}
3. {(3, -4), (5, 2), (3, 8), (6, 7)}
4. {(0, 3), (4, 2), (-1, 7), (0, 3)}
The set {( -4, 2), (3, -2), ( -4, -2), (5, 1)} does not represent a function because it has two different y-values for the x-value of -4.
you can only pick 3 options
Apologies for the confusion. In that case, the three sets of ordered pairs that could represent a function are:
1. {(2, -5), (4, -5), (6, 2), (8, 3)}
2. {(3, -4), (5, 2), (3, 8), (6, 7)}
3. {(0, 3), (4, 2), (-1, 7), (0, 3)}
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.
left-parenthesis 0 comma 1 right-parenthesisImage 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 the ordered pairs are on the graph of the function f(x) = x^2 - 1, we need to substitute the x-values into the function and see if the resulting y-values match the given y-values.
Based on this:
1. (0, 1): f(0) = 0^2 - 1 = -1. This pair is not on the graph of f(x).
2. (1, 0): f(1) = 1^2 - 1 = 0. This pair is on the graph of f(x).
3. (3, 5): f(3) = 3^2 - 1 = 8. This pair is not on the graph of f(x).
4. (5, 24): f(5) = 5^2 - 1 = 24. This pair is on the graph of f(x).
5. (-2, 3): f(-2) = (-2)^2 - 1 = 3. This pair is on the graph of f(x).
6. (-4, -17): f(-4) = (-4)^2 - 1 = 15. This pair is not on the graph of f(x).
Therefore, the ordered pairs (1, 0), (5, 24), and (-2, 3) are on the graph of f(x) = x^2 - 1.
A set of ordered pairs represents a function if each x-value is paired with exactly one y-value.
Let's examine each set of ordered pairs:
1. {(2, -5), (4, -5), (6, 2), (8, 3)}: This set represents a function because each x-value is paired with exactly one y-value.
2. {(-1, 5), (3, 5), (6, 5), (9, 5)}: This set also represents a function because each x-value is paired with exactly one y-value.
3. {(3, -4), (5, 2), (3, 8), (6, 7)}: This set does not represent a function because the x-value 3 is paired with two different y-values (-4 and 8).
4. {(0, 3), (4, 2), (-1, 7), (0, 3)}: This set does not represent a function because the x-value 0 is paired with two different y-values (3 and 3).
5. {(-1, 1), (-1, 6), (-1, 8), (-1, 0)}: This set also does not represent a function because the x-value -1 is paired with four different y-values (1, 6, 8, and 0).
6. {(-4, 2), (3, -2), (-4, -2), (5, 1)}: This set represents a function because each x-value is paired with exactly one y-value.
Therefore, the sets of ordered pairs that represent functions are:
{(2, -5), (4, -5), (6, 2), (8, 3)} and
{(-1, 5), (3, 5), (6, 5), (9, 5)}.
To determine which sets of ordered pairs could represent a function, we need to check if each input value (x-value) in the set has a unique output value (y-value). If every input value has a distinct output value, then the set of ordered pairs represents a function.
Let's examine each set of ordered pairs:
1. {(2, -5), (4, -5), (6, 2), (8, 3)}: In this set, all the x-values have unique corresponding y-values. Therefore, it represents a function.
2. {(-1, 5), (3, 5), (6, 5), (9, 5)}: Here, all the x-values have the same y-value. This set does not represent a function because multiple inputs are mapped to the same output.
3. {(3, -4), (5, 2), (3, 8), (6, 7)}: In this set, the x-value 3 is paired with two different y-values (-4 and 8), which violates the definition of a function. Hence, this set does not represent a function.
4. {(0, 3), (4, 2), (-1, 7), (0, 3)}: The x-value 0 is paired with two different y-values (3 and 7). Therefore, this set does not represent a function.
5. {(-1, 1), (-1, 6), (-1, 8), (-1, 0)}: Similar to the previous set, the x-value -1 is paired with multiple y-values. Thus, this set does not represent a function.
6. {(-4, 2), (3, -2), (-4, -2), (5, 1)}: The x-value -4 has two corresponding y-values (-2 and 2). Therefore, this set does not represent a function.
From the given sets, only the first set {(2, -5), (4, -5), (6, 2), (8, 3)} represents a function.