Directions i dont understand in Algebra 2?

Question

Its in my mathbook:

On many graphing calculators /x/ (the slanted lines are suppose to be absolute values signs) is denoted by ABS(x). use a graphing calculator to graph the absolute value function.
then use the drace feature TO FIND THE CORRESPONDING X VALUES FOR THE GIVEN Y VALUES.


i dont understand the caps part.

heres on of the qustions y=/x+14/ ; y=9


i know how to graph the first equation and then press trace on my graphing calculator but then wuts up with the nine? do i have to do any other math?

Answer 1

it means you need to find the x
for which
|x + 14| = 9
since it is absolute value, you have 2 possibilities:
x + 14 = 9 OR x+ 14 = -9
x = - 5 OR x = - 23

Answer 2

An excessive reliance on calculators can freeze and parch the mind.

It's this simple. From 9 = |x + 14| you get either 9 = x + 14 or 9 = -(x + 14). Even your calculator knows that means either x = -5 or x = -23.