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 Question from Alexis: what does this mean y=|x|-1

Hi Alexis,

The expression $y = |x| - 1$ describes $y$ as a function if $x,$ just as $y = 3x + 4$ and $y = x^2 - 7$ describe $y$ as a function of $x.$ In the case of $y = |x| - 1,$ given a value of $x,$ to calculate the associated value of $y,$ find the absolute value of $x$ and then subtract 1. Thus since $|5| = 5,$ if $x= 5$ then $y = |5| - 1 = 5 - 1 = 4$ and since $|-3| = 3$ if $x = -3$ then $y = |x| - 1 = |-3| - 1 = 3 - 1 = 2.$

When I am introduced a function which is new to me I like to see its graph. I suggest you make a table of some values of $x,$ calculate the associated values of $y,$ plot the points on some graph paper and sketch the graph.

x
y
1
|1| - 1 = 0
2
|2| - 1 = 1
-1
|-1| - 1 = 0
-1/2
|-1/2| - 1 = -1/2
.
.
.
.

Select a few more values of $x,$ extend the table, plot the $(x, y)$ coordinates on some graph paper and sketch the graph.

I hope this helps,
Penny