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 y-intercept. The second graph is steeper than y = |x|.
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 y-intercept of y = |x| is 0, and the x-intercept of the second graph is –15.
explain why
The y-intercept of y = |x| is 0 because when x is equal to 0, the absolute value of x is also 0. This means that the point (0,0) lies on the graph of y = |x|.
On the other hand, the graph of y = |x| - 15 represents the absolute value of x minus 15. To find the x-intercept, we set y equal to 0 and solve for x:
0 = |x| - 15
|x| = 15
Since absolute value is always non-negative, the equation |x| = 15 has two solutions: x = 15 and x = -15. Therefore, the x-intercepts of the graph of y = |x| - 15 are x = 15 and x = -15.
So, the y-intercept of y = |x| is 0, and the x-intercepts of y = |x| - 15 are x = 15 and x = -15. This means the two graphs have different x-intercepts but the same y-intercept, showing they are related but not the same.