Which function could be the parent of y = 3|x| ?
A)y = |x|
B)y = 3x
C)y = x3
D)y = 3 + x
use the same webpage I just gave you
for c) , enter y = x^3
To determine which function could be the parent function of the given function y = 3|x|, we need to find the function that closely resembles the given function without any transformations.
The parent function of y = |x| is the absolute value function, which is represented as y = |x|. It is a V-shaped graph that is symmetrical about the y-axis, with the vertex at (0,0). The absolute value function takes any input, x, and returns the absolute value of x (the positive value of x, regardless of its sign).
Now, let's examine the options:
A) y = |x|: This is indeed the parent function of y = 3|x|. It represents the absolute value function without any transformations.
B) y = 3x: This is a linear function, not the parent function of y = 3|x|. It represents a line with a slope of 3 and intersects the y-axis at the origin.
C) y = x^3: This is a cubic function, not the parent function of y = 3|x|. It represents a graph that forms an S-shape curve.
D) y = 3 + x: This is another linear function, not the parent function of y = 3|x|. It represents a line with a slope of 1 and intersects the y-axis at 3.
Therefore, the correct answer is A) y = |x|.