Question

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.y = |x - 2|

Accepted Answer

Understand the given equation: $$y = |x - 2|$$ represents the absolute value function shifted 2 units to the right along the x-axis. The absolute value function outputs the distance of the input from zero, so it is always non-negative. To create a table of ordered pairs, choose at least three values of $$x$$ around the point where the expression inside the absolute value is zero (i.e., $$x = 2). $$For example, select $$x = 1$$, $$x = 2$$, and $$x = 3. $$Calculate the corresponding $$y$$ values by substituting each chosen $$x$$ into the equation $$y = |x - 2|. $$For each $$x$$, compute $$y as $$the absolute value of $$(x - 2). $$Organize the results into a table of ordered pairs $$(x, y)$$, where each pair satisfies the equation. This table will help visualize the shape of the graph. To graph the equation, plot the ordered pairs on the coordinate plane. Since $$y = |x - 2|$$ forms a 'V' shape, draw two rays: one going upward to the left from the vertex at $$(2, 0)$$ and one going upward to the right from the same vertex.

For each equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation. See Examples 3 and 4.
y = |x - 2|

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Key Concepts

Absolute Value Function

Creating Ordered Pairs from an Equation

Graphing Piecewise Functions