Question

Which phrases describe the graph of f(x) = |x| ? Check all that apply.
V-shaped
U-shaped
opens up
opens down
symmetric with respect to the x-axis
symmetric with respect to the y-axis

Answer 1

V-shaped
opens up
symmetric with respect to the y-axis

Answer 2

Answer:

The correct options are 1, 3 and 6.

Step-by-step explanation:

The given function is

$f(x)=|x|$

It is parent absolute function.

The graph of any absolute function is always V-shaped.

Therefore the graph of f(x) is V-shaped. Option 1 is correct.

If the sign before the modulus is positive, then the graph opens up otherwise it opens down.

In f(x) the sign before the modulus is positive, therefore the graph opens up. Option 3 is correct.

If (x,-y) lies on the function, then f(x) is symmetric with respect to the x-axis.

If (-x,y) lies on the function, then f(x) is symmetric with respect to the y-axis.

Put (x,-y) in the given function.

$-y=|x|\Rightarrow -y\neq y$

Therefore f(x) is not symmetric with respect to the x-axis.

Put (-x,y) in the given function.

$y=|x|\Rightarrow y=y$

Since the point (-x,y) lies on the function, therefore f(x) is symmetric with respect to the y-axis. Option 6 is correct.

Therefore correct options are 1, 3 and 6.