Use the image to answer the question.
An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 7 to 7 in one unit increments. A wavy vertical line is graphed on the coordinate plane. he line passes through points plotted at left parenthesis negative 2 comma negative 3 right parenthesis, left parenthesis negative 1 comma negative 2 right parenthesis, left parenthesis 0 comma negative 1 right parenthesis, and left parenthesis 1 comma 6 right parenthesis.
Determine if the given graph is the graph of the function y=x−1
. Enter 1 for yes. Enter 2 for no.
(1 point)
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page 17 of 18
To determine if the given graph is the graph of the function y=x−1, we can compare the coordinates of the points on the graph with the coordinates we would expect for the function.
For the function y=x-1, if we plug in x=-2, we should get y=-3. However, on the graph, the point (-2,-3) is not on the wavy vertical line.
Similarly, if we plug in x=-1, we should get y=-2. However, the point (-1,-2) is not on the wavy vertical line on the graph.
If we plug in x=0, we should get y=-1. The point (0,-1) is also not on the wavy vertical line.
Finally, if we plug in x=1, we should get y=0. However, the point (1,6) is on the wavy vertical line, which is not the value we would expect based on the function.
Therefore, based on the points plotted on the graph, we can conclude that the given graph is not the graph of the function y=x-1.
Thus, the answer is 2 (no).
To determine if the given graph is the graph of the function y = x - 1, we need to check if the points on the graph satisfy the equation.
Let's check the given points:
(-2, -3): If we substitute x = -2 into the equation y = x - 1, we get y = -2 - 1 = -3. This point satisfies the equation.
(-1, -2): If we substitute x = -1 into the equation y = x - 1, we get y = -1 - 1 = -2. This point also satisfies the equation.
(0, -1): If we substitute x = 0 into the equation y = x - 1, we get y = 0 - 1 = -1. This point satisfies the equation.
(1, 6): If we substitute x = 1 into the equation y = x - 1, we get y = 1 - 1 = 0. This point does not satisfy the equation.
Since one of the points does not satisfy the equation, we can conclude that the given graph is NOT the graph of the function y = x - 1. Therefore, the answer is 2 (no).
To determine if the given graph is the graph of the function y = x - 1, we need to compare the coordinates of the points on the graph with the values of y obtained by substituting the corresponding x-values into the equation.
Let's check each point:
1. (-2, -3)
y = x - 1
Substituting x = -2: y = -2 - 1 = -3
The y-value matches, so this point satisfies the equation.
2. (-1, -2)
y = x - 1
Substituting x = -1: y = -1 - 1 = -2
The y-value matches, so this point satisfies the equation.
3. (0, -1)
y = x - 1
Substituting x = 0: y = 0 - 1 = -1
The y-value matches, so this point satisfies the equation.
4. (1, 6)
y = x - 1
Substituting x = 1: y = 1 - 1 = 0
The y-value does not match. It should be 6, but the equation gives 0.
Since one of the points does not satisfy the equation, the given graph is not the graph of the function y = x - 1. Therefore, the answer is 2 (no).