Question

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

Accepted Answer

Understand the equation given: $$y = |x + 4|. $$This means that for any value of $$x$$, $$y is $$the absolute value of $$x + 4. $$The absolute value function outputs the distance from zero, so $$y is $$always non-negative. To create a table of ordered pairs, choose at least three values for $$x. $$For each $$x$$, calculate $$y by $$evaluating $$y = |x + 4|. $$For example, pick values like $$x = -6$$, $$x = -4$$, and $$x = 0. $$Calculate each corresponding $$y$$ value: For each chosen $$x$$, compute $$y = |x + 4|. $$For instance, if $$x = -6$$, then $$y = |-6 + 4| = |-2|. $$Repeat this for all chosen $$x$$ values to get ordered pairs $$(x, y). $$Organize these ordered pairs into a table format with two columns: one for $$x$$ and one for $$y. $$This table will help visualize the relationship between $$x$$ and $$y. To $$graph the equation, plot each ordered pair from the table on the coordinate plane. Remember that the graph of $$y = |x + 4| is a V-$$shaped graph shifted 4 units to the left from the basic $$y = |x|$$ graph. Connect the points smoothly to form the characteristic V shape.

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

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Key Concepts

Absolute Value Function

Ordered Pairs as Solutions

Graphing Piecewise Functions