Question

1. as jacinta drives to school, the distance she is from a cell phone tower (in miles) is modeled by:

$f(x) =| x - 3 |$
where $x$ is jacinta’s distance from home in miles.
select all statements that are true:
$square$ $f(7) = 4$ means when jacinta is 7 miles from home, she is 4 miles from the cell phone tower.
$square$ $f(7) = 4$ means when jacinta is 7 miles from the cell phone tower, she is 4 miles from home.
$square$ $f(1) = -2$
$square$ $f(1) = 2$
$square$ when jacinta is at home, she is 3 miles from the cell phone tower.

Explanation:

Step1: Analyze \( f(7) \)

Given \( f(x) = |x - 3| \), substitute \( x = 7 \):
\( f(7) = |7 - 3| = |4| = 4 \).
Interpretation: \( x = 7 \) (distance from home), \( f(x) = 4 \) (distance from tower). So " \( f(7)=4 \) means when Jacinta is 7 miles from home, she is 4 miles from the cell phone tower" is true. The second statement about \( f(7)=4 \) misinterprets \( x \) and \( f(x) \), so it's false.

Step2: Analyze \( f(1) \)

Substitute \( x = 1 \):
\( f(1) = |1 - 3| = |-2| = 2 \).
Thus, \( f(1) = -2 \) is false, \( f(1) = 2 \) is true.

Step3: Analyze home case (\( x = 0 \))

Substitute \( x = 0 \) (at home):
\( f(0) = |0 - 3| = 3 \).
Interpretation: When at home (\( x = 0 \)), distance from tower is 3 miles. So "When Jacinta is at home, she is 3 miles from the cell phone tower" is true.

Answer:

• \( f(7) = 4 \) means when Jacinta is 7 miles from home, she is 4 miles from the cell phone tower.
• \( f(1) = 2 \)
• When Jacinta is at home, she is 3 miles from the cell phone tower.