Multiple Choice
Describe how the graphs of y = |x| and y = |x| – 15 are related.
(1 point)
Responses
The graphs have the same shape. The y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15.
The graphs have the same shape. The y -intercept of y = | x | is 0, and the x -intercept of the second graph is –15.
The graphs have the same y-intercept. The second graph is steeper than y = |x|.
The graphs have the same y -intercept. The second graph is steeper than y = | x |.
The two graphs are the same.
The two graphs are the same.
The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is –15.
The graphs have the same shape. The y -intercept of y = | x | is 0, and the y -intercept of the second graph is –15.
The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is –15.
liar
I apologize if my response was not what you were expecting. Can you please clarify which graph options you believe to be correct?
To determine how the graphs of the equations y = |x| and y = |x| – 15 are related, we need to analyze the characteristics of each equation.
The equation y = |x| represents the absolute value of x. This means that the graph will have a V shape and will be symmetrical about the y-axis. The y-intercept of this graph occurs when x = 0, so the point (0, 0) lies on the graph.
The equation y = |x| – 15 includes an additional term subtracted from the absolute value of x. This graph will still have the same shape as y = |x|, but it will be shifted downward by 15 units. The new y-intercept can be found by setting x = 0 in the second equation:
y = |0| – 15
y = -15
Hence, the y-intercept of y = |x| – 15 is (0, -15).
Based on this analysis, the correct choice is:
The graphs have the same shape. The y-intercept of y = |x| is 0, and the y-intercept of the second graph is –15.