Linear vs. nonlinear functions Knowledge-Based Practice

Questions

1. 1.

   What is the difference between the average rate of change of the nonlinear function $g(x) = 2x^2 - 3x$ over the interval $[3, 5]$ and its average rate of change over the interval $[1, 3]$?

   • A) 0
   • B) 4
   • C) 8
   • D) 12
2. 2.

   Let $f(x) = mx + b$ be a linear function with $m \neq 0$. Which of the following operations on $f(x)$ always produces a nonlinear function?

   • A) $g(x) = f(x) + c$ for any real constant $c$
   • B) $g(x) = c \cdot f(x)$ for any nonzero real constant $c$
   • C) $g(x) = f(x + c)$ for any real constant $c$
   • D) $g(x) = [f(x)]^2$
3. 3.

   Which of the following statements is true for every linear function $f(x)$?

   • A) The graph of the function must pass through the origin.
   • B) The value of the output must increase as the input increases.
   • C) Equal changes in the input produce equal proportional ratios in the output.
   • D) The average rate of change between any two distinct points is constant.
4. 4.

   Which of the following sets of ordered pairs can be modeled by a linear function?

   • A) $\{(1, 5), (2, 9), (3, 13), (4, 17)\}$
   • B) $\{(1, 2), (2, 4), (3, 8), (4, 16)\}$
   • C) $\{(1, 1), (2, 4), (3, 9), (4, 16)\}$
   • D) $\{(1, 3), (2, 6), (3, 11), (4, 18)\}$
5. 5.

   Which of the following equations represents a nonlinear function?

   • A) $f(x) = 5 - 3x$
   • B) $g(x) = 3x^2 - 4x + 1$
   • C) $h(x) = \frac{2x - 5}{3}$
   • D) $p(x) = 7x$

Answers and step-by-step solutions appear after you finish the test.