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…

Question

asked Mar 4, 2018 102k views

2 Answers

Sdduursma · Answer 1 · 2018-03-11T02:02:14+0000

Answer:

The correct options are 1, 3 and 6.

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.

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

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.