Question

-

The function f(x) = |x − 1| can be used to determine how far a number 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.
number line showed for reference
←
-5 -4 -3
-2 -1
O
2 3
f(-5) =
meaning the number
from 1 on the number line. This interpretation
context of the problem.
f(3) =
1 on the number line. This interpretation
the problem.
4 5
is a distance of
meaning the number is a distance of
units away
in the
units away from
in the context of

Answer 1

Explanation:

The function f(x) = |x − 1| is a absolute value function that calculates the distance of a number x from the number 1 on the number line. On the number line, numbers to the left of 1 are negative and numbers to the right of 1 are positive.

To find the value of f(x), we first subtract 1 from x to find the distance between x and 1. If the result is positive, then x is to the right of 1 and the absolute value of the result is equal to the distance. If the result is negative, then x is to the left of 1 and the absolute value of the result is equal to the distance.

For example, let's find f(-5):

f(-5) = |-5 - 1| = |-6| = 6

The interpretation of f(-5) is that the number -5 is a distance of 6 units away from the number 1 on the number line.

Now let's find f(3):

f(3) = |3 - 1| = |2| = 2

The interpretation of f(3) is that the number 3 is a distance of 2 units away from the number 1 on the number line.

The domain of the function is all real numbers. The range of the function is all non-negative real numbers.