Question

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

Accepted Answer

Identify the domain of the function $$y = \sqrt{x - 3}. $$Since the expression inside the square root must be non-negative, set $$x - 3 \geq 0$$, which means $$x \geq 3. $$Choose at least three values of $$x$$ that satisfy the domain condition (i.e., $$x \geq 3). $$For example, select $$x = 3$$, $$x = 4$$, and $$x = 7. $$Calculate the corresponding $$y$$ values by substituting each chosen $$x$$ into the equation $$y = \sqrt{x - 3}. $$For instance, for $$x=3$$, compute $$y = \sqrt{3 - 3}$$; for $$x=4$$, compute $$y = \sqrt{4 - 3}$$; and for $$x=7$$, compute $$y = \sqrt{7 - 3}. $$Create a table of ordered pairs $$(x, y)$$ using the values found in the previous step. This table will show at least three points that lie on the graph of the equation. To graph the equation, plot the ordered pairs from the table on the coordinate plane. Then, draw a smooth curve starting at the point where $$x=3 ($$the domain's start) and continuing to the right, reflecting the shape of the square root function.

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

Key Concepts

Domain of a Function

Evaluating Functions and Ordered Pairs

Graphing Square Root Functions