Question

the function ( f(x)=|x - 1| ) can be used to determine how far a number ( x ) is away from the number 1 on the number line. find and interpret the given function values and determine an appropriate domain for the function.

based on the observations above, it is clear that an appropriate domain for the function is all real numbers

adswer attempt 1 out of 2

( f(-5)=square ), meaning the number ( square ) is a distance of ( square ) units away from 1 on the number line. this interpretation

( f(3)=square ), meaning the number ( square ) is a distance of ( square ) units away from 1 on the number line. this interpretation

( f(4.5)=square ), meaning the number ( square ) is a distance of ( square ) units away from 1 on the number line. this interpretation

in the context of the problem.

in the context of the problem.

in the context of the problem.

Explanation:

Step1: Calculate \( f(-5) \)

The function is \( f(x)=\vert x - 1\vert \). Substitute \( x=-5 \) into the function:

$$
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$$

This means the number \( -5 \) is a distance of \( 6 \) units away from \( 1 \) on the number line.

Step2: Calculate \( f(3) \)

Substitute \( x = 3 \) into the function \( f(x)=\vert x - 1\vert \):

$$
LATEXBLOCK1
$$

This means the number \( 3 \) is a distance of \( 2 \) units away from \( 1 \) on the number line.

Step3: Calculate \( f(4.5) \)

Substitute \( x = 4.5 \) into the function \( f(x)=\vert x - 1\vert \):

$$
LATEXBLOCK2
$$

This means the number \( 4.5 \) is a distance of \( 3.5 \) units away from \( 1 \) on the number line.

Answer:

\( f(-5)=6 \), the number \( -5 \) is a distance of \( 6 \) units away from \( 1 \) on the number line; \( f(3)=2 \), the number \( 3 \) is a distance of \( 2 \) units away from \( 1 \) on the number line; \( f(4.5)=3.5 \), the number \( 4.5 \) is a distance of \( 3.5 \) units away from \( 1 \) on the number line.