Question

Make a table of values, and sketch the graph of the equation.

$y=\left|x\right|-1$

Short answer

The graph of the equation$y=\left|x\right|-1$ s provided below.

Step-by-step solution

Step 1. Apply the concept of coordinates.

The set of all points$\left(x,y\right)$ in the Cartesian plane or coordinate plane that satisfy the equation is known as the graph of the equation in x and y coordinates.

Step 2. Construct a table of values.

Consider the provided equation $y=\left|x\right|-1$.

The absolute value of a function is expressed as, if x is a real number then the absolute value of xis defined as.

$\left|x\right|=x$ when x is greater than or equal to 0. In other words, the absolute value of x is x when x is either positive or zero.

$\left|x\right|=-x$ when x is less than 0. In other words, the absolute value of x is the opposite of x when x is negative.

Consider real values for x and corresponding to it find the values of y.

$\begin{array}{ccc}x& y=\left|x\right|-1& \left(x,y\right)\\ -2& 1& \left(-2,1\right)\\ -1& 0& \left(-1,0\right)\\ 0& -1& \left(0,-1\right)\\ 1& 0& \left(1,0\right)\\ 2& 1& \left(2,1\right)\end{array}$

Step 3. Graph the equation.

Plot the ordered pairs on the Cartesian plane to obtain the graph of the equation .

$y=\left|x\right|-1$