Question

The graph of an absolute value function contains the points (–3, 5), (0, 2) and (3, 5). Which could be the function represented by this graph? Check all that apply.
f(x) = |x| + 2
f(x) = –|x| + 2
f(x) = |x| – 2
f(x) = |–x + 2|
f(x) = |–x| + 2
f(x) = –|x| – 2
f(x) = |x + 2|

Answer 1

The absolute value functions that contains the points are:

• f(x) = |x| + 2
• f(x) = |-x| + 2

Which could be the function represented by this graph?

Here we have the points (-3, 5), (0, 2), and (3, 5). We want to see which ones of the given functions have that points.

To check that, we need to evaluate the functions in the first value of each point and see if the outcome is the second value of the correspondent point.

For example, for the first equation:

• f(-3) = |-3| + 2 = 5   so it has the point (-3, 5)
• f(0) = |0| + 2 = 2  so it has the point (0, 2)
• f(3) = |3| + 2 = 5  so it has the point (3, 5).

The other option that also contains these 3 points is:

f(x) = |-x| + 2

• f(-3) = |3| + 2 = 5  so it has the point (-3, 5)
• f(0) = |-0| + 2 = 2  so it has the point (0, 2)
• f(3) =  |-3| + 2 = 5  so it has the point (3, 5).

And all the other options can be trivially discarded (by evaluating them).

So the two correct options are:

• f(x) = |x| + 2
• f(x) = |-x| + 2

If you want to learn more about absolute value functions:

brainly.com/question/3381225

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