Lesson 115: Graphing Cubic Functions — Practice Questions

1. 1. Which of the following equations represents a cubic function?

   • A. $y = x^2 + 5$
   • B. $y = 3x + 1$
   • C. $y = x^3 - 2$
   • D. $y = 5$

2. 2. The volume $V$ of a cube with side length $s$ is given by the function $V = s^3$. If a cube has a side length of 5 inches, its volume is ___ cubic inches.

3. 3. Consider the parent cubic function $f(x) = x^3$. What is the value of $f(x)$ when $x = -3$?

4. 4. A common mistake when evaluating an expression like $2^3$ is to calculate $2 \times 3$. What is the correct value of $2^3$?

   • A. 6
   • B. 5
   • C. 8
   • D. 9

5. 5. For the parent cubic function $y = x^3$, which of these statements correctly describes a property of its graph?

   • A. If x is negative, y is positive.
   • B. The graph passes through the point (0, 0).
   • C. The graph does not have any negative y-values.
   • D. The graph is a straight line.

6. 6. To solve the equation $x^3 + 5x = 10$ by finding the x-intercepts of a single graph, which function should you graph?

   • A. $y = x^3 + 5x + 10$
   • B. $y = x^3 - 5x + 10$
   • C. $y = x^3 + 5x - 10$
   • D. $y = 10 - 5x$

7. 7. By testing integer values for x, find the exact real solution to the equation $x^3 + 2x = 3$. The solution is $x = \_\_\_$.

8. 8. The real solution to the equation $x^3 - 3x = 7$ lies between which two consecutive integers?

   • A. Between $x=1$ and $x=2$
   • B. Between $x=2$ and $x=3$
   • C. Between $x=3$ and $x=4$
   • D. Between $x=0$ and $x=1$

9. 9. To solve the equation $x^3 = 2x + 1$ by graphing, you rewrite it to define the function $y = x^3 - 2x - 1$. What is the value of $y$ when $x=2$?

10. 10. To solve $3x^3 = 9$ by graphing, we graph $y = 3x^3 - 9$. The solution to the original equation is found at the graph's x-intercept. Why is this true?

    • A. Because the x-intercept is where the function has its minimum value.
    • B. Because the x-intercept is where $x=0$.
    • C. Because the x-intercept is the point where $y=0$, which makes $3x^3 - 9 = 0$.
    • D. Because the x-intercept is always an integer.