Comparing and modeling functions Knowledge-Based Practice

Questions

1. 1.

   Two functions are defined by $f(x) = 2^{x-3} - 16$ and $g(x) = \log_3(x - 2) - 2$. What is the sum of their $x$-intercepts?

   • A) 15
   • B) 16
   • C) 18
   • D) 20
2. 2.

   Two functions are defined by $f(x) = -x^2 + 6x - 5$ and $g(x) = x + 1$. On which open interval does the graph of $f(x)$ lie strictly above the graph of $g(x)$?

   • A) $(1, 5)$
   • B) $(-3, -2)$
   • C) $(2, 3)$
   • D) $(-\infty, 2) \cup (3, \infty)$
3. 3.

   A linear model $f(t) = at + b$ and an exponential model $g(t) = c \cdot d^t$ with $d > 0$ both satisfy $f(0) = g(0) = 12$ and $f(2) = g(2) = 48$. What is the value of $g(3) - f(3)$?

   • A) 24
   • B) 30
   • C) 36
   • D) 42
4. 4.

   Two functions are defined by $f(x) = -(x - 3)^2 + 16$ and $g(x) = 2x^2 - 8x + 3$. What is the difference between the maximum value of $f(x)$ and the minimum value of $g(x)$, evaluated as $\max(f) - \min(g)$?

   • A) 21
   • B) 11
   • C) 13
   • D) -21
5. 5.

   Two functions are defined by $f(x) = 5x + 12$ and $g(x) = 2x^2 - 3x + 4$. Which statement correctly compares their average rates of change over the closed interval $[1, 4]$?

   • A) The average rate of change of $f(x)$ is greater than that of $g(x)$ by 2.
   • B) The average rate of change of $f(x)$ is equal to that of $g(x)$.
   • C) The average rate of change of $g(x)$ is greater than that of $f(x)$ by 2.
   • D) The average rate of change of $g(x)$ is greater than that of $f(x)$ by 4.

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