Which of the following is the point on the graph described as the function y=(2x+1)2-4
A 1,-5
B 0,-2
C 1,2
D -1,-3
To find the point on the graph described by the function y=(2x+1)2-4, we need to substitute the x-coordinate into the function and solve for y.
A) (1,-5):
- Substitute x=1 into the function:
y=(2(1)+1)^2-4
y=(2+1)^2-4
y=3^2-4
y=9-4
y=5
Therefore, the point (1,-5) is NOT on the graph.
B) (0,-2):
- Substitute x=0 into the function:
y=(2(0)+1)^2-4
y=(0+1)^2-4
y=1^2-4
y=1-4
y=-3
Therefore, the point (0,-2) is NOT on the graph.
C) (1,2):
- Substitute x=1 into the function:
y=(2(1)+1)^2-4
y=(2+1)^2-4
y=3^2-4
y=9-4
y=5
Therefore, the point (1,2) is NOT on the graph.
D) (-1,-3):
- Substitute x=-1 into the function:
y=(2(-1)+1)^2-4
y=(-2+1)^2-4
y=(-1)^2-4
y=1-4
y=-3
Therefore, the point (-1,-3) is on the graph.
Therefore, the correct answer is D) -1,-3.
Which of the following is a graph of the function
Y= x +2
Apologies, the list of answer choices for this question is missing. In order to determine which graph represents the function y = x +2, we need to look for the graph that is a straight line with a slope of 1 and a y-intercept of 2. This equation is in slope-intercept form y = mx + b, where m represents the slope and b represents the y-intercept.
Here is a description of the graph of y = x +2:
- It is a straight line.
- It has a slope of 1, which means it increases by 1 unit in the y-direction for every 1 unit increase in the x-direction.
- It has a y-intercept of 2, which means it crosses the y-axis at the point (0, 2).
Without the list of answer choices, it is not possible to identify which graph accurately represents the function y = x +2.
Which of the following is two quantities whose function relationship is described in the given graph
Apologies, but I cannot determine the answer without the given graph or the list of answer choices. Please provide more information.
To find the point on the graph described by the function y=(2x+1)²-4, we need to substitute different values of x and solve for y.
Let's substitute each of the given x values into the function and calculate y:
For point A: x = 1
y = (2(1) + 1)² - 4
y = (2 + 1)² - 4
y = (3)² - 4
y = 9 - 4
y = 5
For point B: x = 0
y = (2(0) + 1)² - 4
y = (0 + 1)² - 4
y = (1)² - 4
y = 1 - 4
y = -3
For point C: x = 1
y = (2(1) + 1)² - 4
y = (2 + 1)² - 4
y = (3)² - 4
y = 9 - 4
y = 5
For point D: x = -1
y = (2(-1) + 1)² - 4
y = (-2 + 1)² - 4
y = (-1)² - 4
y = 1 - 4
y = -3
From the calculations, we can see that only point C has the correct pair of x and y values, which is (1, 5). Therefore, the point on the graph described by the function is C, 1,2.