Lesson 4: Comparing Linear and Nonlinear Functions — Practice Questions

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

   • A. $y = 3x - 5$
   • B. $y = \frac{x}{2}$
   • C. $y = x^2 - 1$
   • D. $y = 7$

2. 2. Which equation represents a linear function?

   • A. $y = 3^x$
   • B. $y = 5 - 2x$
   • C. $y = \sqrt{x} + 4$
   • D. $y = \frac{1}{x}$

3. 3. The equation $y = 7x + 2$ represents a ___ function. (linear/nonlinear)

4. 4. Because the variable $x$ is in the exponent, the equation $y = 5^x - 1$ represents a ___ function. (linear/nonlinear)

5. 5. Which of the following equations can be rearranged to represent a linear function?

   • A. $y = 9x^2$
   • B. $y = 3^x$
   • C. $y - 4x = 1$
   • D. $y = \sqrt{x}$

6. 6. Which of the following scenarios describes a linear function?

   • A. The area $A$ of a circle with a given radius $r$, where $A = \pi r^2$.
   • B. The total cost $C$ to buy $n$ notebooks that cost 3 dollars each, where $C = 3n$.
   • C. The volume $V$ of a cube with a given side length $s$, where $V = s^3$.
   • D. The surface area $S$ of a cube with a given side length $s$, where $S = 6s^2$.

7. 7. The area $A$ of a circle with radius $r$ is given by the equation $A = \pi r^2$. This function is nonlinear because the variable $r$ is raised to the power of ___.

8. 8. A taxi service charges a $\$2.00$ flat fee plus $\$3.00$ per mile. The cost $C$ for a ride of $d$ miles is $C = 3d + 2$. Is the relationship between cost and distance linear or nonlinear?

   • A. Linear
   • B. Nonlinear

9. 9. The perimeter $P$ of a regular pentagon with side length $s$ is given by the linear equation $P = 5s$. If this equation is written in the form $y = mx + b$, the value of $m$ is ___.

10. 10. The volume $V$ of a sphere is given by the equation $V = \frac{4}{3}\pi r^3$, where $r$ is the radius. Why is this function considered nonlinear?

    • A. Because it includes the constant $\pi$.
    • B. Because the equation involves a fraction.
    • C. Because the variable $r$ is raised to the power of 3.
    • D. Because the volume must be a positive number.