Answer
Option C is correct.
The set of ordered pairs that make up points on the graph of the function y = 3x³ + 5x² + 9x + 7 is (-1,0), (0,7), (1, 24), (2, 69).
Explanation
The question is
y = 3x³ + 5x² + 9x + 7
We are then told to select the set of ordered pairs that make up points on the graph.
To solve this, you need to first know that the ordered pairs are usually written in coordinates format, meaning that the format in which they are written is (x, y),
For example, (1, 2) means that at the point given, x = 1 and y = 2.
So, the set of ordered pairs that will be the answer will have all of the points in that option satisfying the given equation.
This means that we need to go from one option to the other to check which one is correct.
The equation to be satisfied is
y = 3x³ + 5x² + 9x + 7
Starting with option A
(-1, 13), (0, 14), (1, 24), (2, 69)
For this to be the answer, each of the four ordered pairs must satisfy the equation given
Taking the first ordered pair first (-1, 13)
(-1, 13) means that when x = -1, y = 13
y = 3x³ + 5x² + 9x + 7
y = 3(-1)³ + 5(-1)² + 9(-1) + 7
y = 3(-1) + 5(1) + 9(-1) + 7
y = -3 + 5 - 9 + 7 = 0
0 is not equal to 13.
This means that option A cannot be the answer since one of its ordered pairs do not satisfy the equation.
On to option B
(-1, -10), 0,7), (1, 10), (2, 56)
Taking the first ordered pair first, (-1, -10)
(-1, -10) means that when x = -1, y = -10
y = 3x³ + 5x² + 9x + 7
We already calculated above (under the calculation for option A) that when x = -1, y = 0.
0 is not equal to -10.
This means that option B cannot be the answer since one of its ordered pairs do not satisfy the equation.
On to option C
(-1,0), (0,7), (1, 24), (2, 69)
Taking the first ordered pair first, (-1, 0)
(-1, 0) means that when x = -1, y = 0.
y = 3x³ + 5x² + 9x + 7
We already know that for this expression, when x = -1, y is indeed equal to 0.
So, we move on to the second ordered pair, (0, 7)
(0, 7) means that when x = 0, y = 7
y = 3x³ + 5x² + 9x + 7
y = 3(0)³ + 5(0)² + 9(0) + 7
y = 3(0) + 5(0) + 9(0) + 7
y = 0 + 0 + 0 + 7 = 7
The second ordered pair also satisfies this equation.
So, we move on to the third ordered pair, (1, 24)
(1, 24) means that when x = 1, y = 24
y = 3x³ + 5x² + 9x + 7
y = 3(1)³ + 5(1)² + 9(1) + 7
y = 3(1) + 5(1) + 9(1) + 7
y = 3 + 5 + 9 + 7 = 24
The third ordered pair also satisfies the equation.
It is actually clear now that this option C will have all of its pairs satisfying the equation, but let us just do the same for the fourth ordered pair to be absolutely sure.
The fourth ordered pair is (2, 69)
(2, 69) means when x = 2, y = 69
y = 3x³ + 5x² + 9x + 7
y = 3(2)³ + 5(2)² + 9(2) + 7
y = 3(8) + 5(4) + 9(2) + 7
y = 24 + 20 + 18 + 7 = 69
The fourth ordered pair also satisfies the equation like we predicted.
Hence, the set of ordered pairs that make up points on the graph of the function y = 3x³ + 5x² + 9x + 7 is (-1,0), (0,7), (1, 24), (2, 69).
Option C is correct!
Hope this Helps!!!