Math Problem Statement
Complete the table of values for y = x^3 + x - 2 and draw the graph for values of x from -2 to 2.
Solution
The problem asks you to complete the table and graph the function for values from to .
Step 1: Calculate values for values from to .
The equation is:
For :
For :
For :
For :
For :
Step 2: Complete the Table
The completed table is:
\hline x & y \\ \hline -2 & -12 \\ -1 & -4 \\ 0 & -2 \\ 1 & 0 \\ 2 & 8 \\ \hline \end{array}$$ ### Step 3: Plot the Graph On the graph: 1. Plot the points $$(-2, -12)$$, $$(-1, -4)$$, $$(0, -2)$$, $$(1, 0)$$, and $$(2, 8)$$. 2. Connect these points with a smooth curve since $$y = x^3 + x - 2$$ is a cubic function. Would you like further help with plotting or interpreting the graph? ### Related Questions: 1. What is the behavior of cubic functions as $$x \to \infty$$ and $$x \to -\infty$$? 2. How do changes to the constant term in $$y = x^3 + x - 2$$ affect the graph? 3. Can you identify turning points of the function $$y = x^3 + x - 2$$? 4. What is the significance of the $$y$$-intercept in this context? 5. How does the coefficient of $$x^3$$ influence the steepness of the curve? ### Tip: When sketching cubic graphs, remember that they can have up to two turning points, and the end behavior depends on the sign of the leading coefficient.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Cubic Functions
Graphing
Table of Values
Formulas
y = x^3 + x - 2
Theorems
Behavior of polynomial functions
Suitable Grade Level
Grades 9-12