Below are the functions of y=|x| and y=|x|-5. how are the functions related?
A. the functions have the same shape. the y-intercept of y=|x| is 0 and the y-intercept of the second function is 5
B. the functions have the same y-intercept. the second function is steeper than y=|x|
C. the two functions are the same.
D. the functions have the same shape. the y-intercept of y=|x| is 0, and the y-intercept of the second function is -5
scott don't be weird. Give us the answer please:)
Well, you're in luck! I have the answer for you, with a sprinkle of humor on top. The correct answer is D. the functions have the same shape. The y-intercept of y=|x| is 0, and the y-intercept of the second function is -5. So, the only thing that changed is that the second function went on a little vacation and took a trip down south, landing at -5. They still have the same shape, like two peas in a pod, or two clowns in a circus! Why change something that's already working?
The correct answer is D. The functions have the same shape, and the y-intercept of y = |x| is 0, while the y-intercept of the second function is -5.
To determine how the functions y=|x| and y=|x|-5 are related, let's analyze each option:
A. The functions have the same shape. The y-intercept of y=|x| is 0, and the y-intercept of the second function is 5.
To verify this option, we need to understand the characteristics of the absolute value function. The absolute value function, y=|x|, has a V-shaped graph centered at the origin (0,0). It starts at the origin and extends upwards, symmetrically to the negative x-axis. The y-intercept of y=|x| is indeed 0, which aligns with the given statement. However, the y-intercept of y=|x|-5 is -5, not 5. Thus, option A is incorrect.
B. The functions have the same y-intercept. The second function is steeper than y=|x|.
To evaluate this option, we need to examine the second function, y=|x|-5. By subtracting 5 from the absolute value, the entire graph is shifted downward by 5 units. This transformation does not affect the y-intercept but rather shifts the entire graph vertically. Therefore, the second function also has a y-intercept of 0, identical to y=|x|. However, there is no mention about one function being steeper than the other. Hence, option B is incorrect.
C. The two functions are the same.
This option claims that y=|x| and y=|x|-5 are identical, which is not the case. As we discussed earlier, subtracting 5 from the absolute value function shifts the entire graph downwards. Therefore, option C is incorrect.
D. The functions have the same shape. The y-intercept of y=|x| is 0, and the y-intercept of the second function is -5.
This option accurately describes the relationship between the two functions. As explained in option A, both functions have the same shape, but the second function, y=|x|-5, is shifted downwards by 5 units. This downward shift is evident from the y-intercept of -5 in the second function compared to the origin (0,0) in y=|x|. Therefore, option D is correct.
Thus, the correct answer is D. The functions have the same shape. The y-intercept of y=|x| is 0, and the y-intercept of the second function is -5.