Answer: The graph has a line of symmetry at y = 0.
Step-by-step explanation:
I suppose that this refers to the function:
f(x) = IxI
The parent absolute value function.
Remember how this works:
IxI = x if x ≥ 0
IxI = -x if x ≤ 0.
Let's analyze the sentences:
1) "The x- and y-intercepts are (0,0)"
This is true, when x = 0 we have:
y = f(0) = I0I = 0
So the point (0, 0) is the only x-intercept and the only y-intercept.
2) "Domain: (-∞,∞); Range: [0,∞)"
This is also true, we clearly do not have any restriction in the domain.
And when looking at the range, we can see that the possible values of y are always positive or zero.
3) "(0, 0) is the minimum point."
Now, as x increases in the positive range, also does the value of y.
And as x decreases in the negative range, as the absolute value changes the sign, we will also have an increase in the value of y.
Then we have that (0, 0) must be the minimum.
4) "The graph has a line of symmetry at y = 0."
This is false.
The real line of symmetry is at x = 0, y = 0 corresponds to the x-axis, and as the graph opens up, we can not have symmetry about any line parallel to the x-axis.
