Lesson 3: Function Notation — Practice Questions

1. 1. For the function defined by $x = h(v) = 2v^2 - 3v + 1$, which variable is the input and which is the output?

   • A. Input: $v$, Output: $x$
   • B. Input: $x$, Output: $v$
   • C. Input: $h$, Output: $v$
   • D. Input: $v$, Output: $h$

2. 2. For the function defined by $A = g(r) = 750(1 + r)^2$, which variable is the input and which is the output?

   • A. Input: $r$, Output: $A$
   • B. Input: $A$, Output: $r$
   • C. Input: $g$, Output: $A$
   • D. Input: $r$, Output: $g$

3. 3. In the function notation $f(x)$, what does the variable $x$ represent?

   • A. The name of the function
   • B. The output of the function
   • C. The input of the function
   • D. A constant value

4. 4. A function $P(t) = 150t - 400$ models the profit, in dollars, from selling $t$ tickets. The statement $P(20) = 2600$ means that the profit from selling 20 tickets is ___ dollars.

5. 5. A function is defined by the equation $V = f(s) = s^3$, where $V$ is the volume of a cube and $s$ is its side length. Which variable represents the input?

   • A. V
   • B. f
   • C. s
   • D. $s^3$

6. 6. Which statement best describes the meaning of the parentheses in the notation $g(x)$?

   • A. They indicate that $g$ should be multiplied by $x$.
   • B. They enclose the input value for the function $g$.
   • C. They represent the output of the function $g$.
   • D. They are used to group terms for the order of operations.

7. 7. Given the function $f(x) = 4x - 5$, find the value of $x$ for which $f(x) = 11$. The value of $x$ is ___.

8. 8. If $g(t) = -3t + 15$, for what value of $t$ is $g(t) = 3$?

   • A. 3
   • B. 4
   • C. 6
   • D. -6

9. 9. For the function $h(x) = \frac{1}{3}x + 1$, find the value of $x$ such that $h(x) = 6$. The value of $x$ is ___.