Question

Which statements are true for the function y= \xi - 2? Select all that apply. The value of the function is never negative. Its graph has a V-shape There is only one input for which the output is 0. There are two inputs for which the output is 5 The vertex. of ts graph 13 81 (0.-2).

Answer 1

Step-by-step explanation:

We need to check out each of the options to determine which of the statements are true:

The given function: y = |x| - 2

a) The symbol '| |' means absolute. So any number you put in it either positive or negative number,becomes positive after it is removed.

For example: if x = -2, y = |-2| - 2 = 2 -2 = 0

if x = -1, y = |-1| -2 = 1 -2 = -1

Hence from the example above, the value of the function can be negative.

Statement is wrong

b) Yes, the graph has a V shape: (statement is correct)

c) For the output to be 0, it means y = 0

Let's find out the value of x when y= 0

y = |x| -2

0 = |x| -2

0 + 2 = |x|

|x| = 2

|x| = x or -x

From the above we have only one x value (the input) which is 2

Statement is correct

d) For the output to be 5, y = 5

5 = |x| -2

|x| = -2 -5

|x| = -7

|x| = x or -x

x = -7 or -x = -7

x = -7 or x = 7