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 - 3)

Accepted Answer

Step 1: Understand the equation given: $$y = \sqrt{x} - 3. $$This means for each value of $$x$$, $$y is $$the square root of $$x$$ minus 3. Note that $$x$$ must be greater than or equal to 0 because the square root function is only defined for non-negative numbers in the real number system. Step 2: Create a table of ordered pairs $$(x, y) by $$choosing at least three values of $$x$$ that are greater than or equal to 0. For each chosen $$x$$, calculate $$y$$ using the formula $$y = \sqrt{x} - 3. $$For example, pick $$x = 0$$, $$x = 1$$, and $$x = 4 as $$starting points. Step 3: Calculate the corresponding $$y$$ values for each $$x$$ chosen: For $$x=0$$, $$y = \sqrt{0} - 3$$; for $$x=1$$, $$y = \sqrt{1} - 3$$; for $$x=4$$, $$y = \sqrt{4} - 3. $$Write these as ordered pairs $$(0, y_0$)$$, $$(1, y_1$)$$, and $$(4, y_4$). $$Step 4: Extend the table if needed by choosing additional $$x$$ values to better understand the shape of the graph. Remember, the domain is $$x \geq 0. $$Step 5: To graph the equation, plot the ordered pairs from your table on the coordinate plane. Since $$y = \sqrt{x} - 3 is a $$transformation of the basic square root function $$y = \sqrt{x}$$ shifted down by 3 units, the graph will start at $$(0, -3)$$ and increase slowly as $$x$$ increases.

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 - 3)

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Domain of a Function

Square Root Function

Plotting Ordered Pairs and Graphing