Question

Select the correct answer.

Consider the function given below.
f(x) = lx-5l +2
Which of the following statements about the y-values of the graph of the function is true?
A. The y-values are all greater than or equal to 5.
B. The y-values are all greater than or equal to 2.
C. The y-values are all less than or equal to 2.
D. The y-values are all less than or equal to 5.

Answer 1

Explanation:

the list of your answer options has a different sequence than the picture.

I assume the picture shows us the correct sequence.

the correct answer is

D : the y-values are all greater than our equal to 2

why ?

because the term in absolute value can only go down to 0 but not below. it is an absolute value after all : it is always positive (minimum 0), no matter what.

so, the minimum value of the function is 0 + 2 = 2. it cannot get lower than this.

Answer 2

The y-values are all greater than or equal to 2.

Explanation:

The absolute value function |x - 5| represents the distance between x and 5 on the number line. Regardless of whether x is greater or less than 5, the absolute value |x - 5| will always be non-negative.

Therefore, for any real number x:

`\large\textx - 5`

When we add 2 to this non-negative value, we will always get a y-value that is greater than or equal to 2 because we're adding a positive number to a non-negative number.

`\large\textx - 5`

`\large\text+2 \geq 2$`

Therefore, the correct statement is:

• The y-values are all greater than or equal to 2.