2-3 Linearity and Continuity of Graphs — Practice Questions

1. 1. A function's graph is a horizontal line. What can you conclude about this function?

   • A. It is linear.
   • B. It is nonlinear.
   • C. It is a parabola.
   • D. It cannot be determined.

2. 2. If a function has a rate of change that is not constant, what would its graph look like?

   • A. A straight line
   • B. A horizontal line
   • C. A curve
   • D. A vertical line

3. 3. A function is graphed and it is a straight line with a negative slope, similar to the graph of $y = -x + 3$. Is this function linear or nonlinear?

   • A. Linear
   • B. Nonlinear

4. 4. Which of the following best describes the graph of a linear function?

   • A. A curve
   • B. A non-vertical straight line
   • C. A circle
   • D. A set of disconnected points

5. 5. The graph of a certain function is a smooth curve that is not straight. What type of function is it?

   • A. Linear
   • B. Nonlinear

6. 6. A linear function is defined by $f(x) = 4x - 5$. What is the constant rate of change for this function between any two points? The rate of change is ___.

7. 7. Consider the functions $f(x) = 3x$ and $g(x) = x^2$. Which statement correctly compares their average rates of change?

   • A. The rate of change of $f(x)$ is constant, while the rate of change of $g(x)$ is variable.
   • B. The rate of change of $g(x)$ is constant, while the rate of change of $f(x)$ is variable.
   • C. Both functions have a constant rate of change.
   • D. Both functions have a variable rate of change.

8. 8. What is the average rate of change for the nonlinear function $h(x) = x^2 + 1$ over the interval from $x=2$ to $x=5$? The average rate of change is ___.

9. 9. Plan A offers a salary of 60,000 dollars with a 2,000 dollar raise each year. Plan B offers 60,000 dollars with a 3% raise each year. Which statement is true?

   • A. Plan A represents linear growth, and Plan B represents nonlinear growth.
   • B. Plan A represents nonlinear growth, and Plan B represents linear growth.
   • C. Both plans represent linear growth.
   • D. Both plans represent nonlinear growth.

10. 10. A car moving at a constant velocity is described by the linear function $d = 55t$. A car that is accelerating is described by $d = 12t^2$. Which car has a constant rate of change of distance over time?

    • A. The car moving at constant velocity
    • B. The accelerating car
    • C. Both cars
    • D. Neither car