Comparing and modeling functions Knowledge-Based Download PDF

Questions

1. 1.

   What is the maximum vertical distance between the graphs of the functions $f(x) = -x^2 + 7x + 2$ and $g(x) = 3x - 10$ on the interval where $f(x) \ge g(x)$?

   • A) 12
   • B) 14
   • C) 16
   • D) 18
2. 2.

   The functions $f(x) = x^2 - 4x + 7$ and $g(x) = 3^{x-1} + 1$ are defined on the interval $[0, 3]$. What is the difference between the maximum value of $g(x)$ and the minimum value of $f(x)$ on this interval?

   • A) 7
   • B) 6
   • C) 4
   • D) 3
3. 3.

   A linear model $L(x)$ increases by a constant rate of 5 units per unit increase in $x$ with $L(0) = 12$, and a quadratic model $Q(x)$ with $Q(0) = 12$ reaches its maximum value of 28 at $x = 4$. What is the positive value of $x$ for which $L(x) = Q(x)$?

   • A) 1.5
   • B) 2
   • C) 2.5
   • D) 3
4. 4.

   A linear model $f(x) = mx + b$ and an exponential model $g(x) = a \cdot r^x$ (where $r > 0$) satisfy the conditions $f(0) = g(0) = 40$, $f(2) = 100$, and $g(2) = 160$. What is the value of $g(3) - f(3)$?

   • A) 150
   • B) 170
   • C) 190
   • D) 210
5. 5.

   Two functions are defined as $f(x) = 2x^2 - x + 3$ and $g(x) = 3 \cdot 2^x - 1$. Over the interval $[1, 3]$, by how much does the average rate of change of $g(x)$ exceed the average rate of change of $f(x)$?

   • A) 8
   • B) 5
   • C) 4
   • D) 2