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 = x³

Accepted Answer

Understand the given equation: $$y = x^3$ represents a cubic function where the output y$ is the cube of the input x$. This means for any value of x$, y$ is calculated by multiplying x$ by itself three times. Create a table of values by choosing at least three different values for x$. For each chosen x$, calculate y$ using the formula y$$ = $$x^3. $$For example, select values such as $$x = -2$$, $$x = 0$$, and $$x = 2. $$Calculate the corresponding $$y$$ values for each $$x$$: For $$x = -2$$, compute $$y = (-2)^3$; for x = 0$, compute y$$ = $$0^3$$; and for $$x = 2$$, compute $$y = 2^3$. These ordered pairs (x$$, y)$$ will be points on the graph. Organize these ordered pairs into a table format with two columns labeled x$ and y$, listing each pair as a solution to the equation. To graph the equation, plot each ordered pair from the table on the coordinate plane. Connect the points smoothly, noting that the graph of y$$ = $$x^3 is a $$curve that passes through the origin and has an S-shape, increasing steeply for positive $$x$$ and decreasing steeply for negative $$x.$$

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 = x³

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Understanding the Equation y = x³

Creating Ordered Pairs from a Function

Graphing Cubic Functions