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3-6 Piecewise and Step Functions — Practice Questions

  1. 1. Consider the function $h(x) = \begin{cases} 4 & \text{if } 0 \leq x < 2 \\ 7 & \text{if } 2 \leq x < 5 \\ 3 & \text{if } 5 \leq x < 8 \end{cases}$. The value of $h(5)$ is ___.

  2. 2. A parking garage charges fees based on the function $P(t)$, where $t$ is hours: $P(t) = \begin{cases} 4 & \text{if } 0 < t \leq 2 \\ 7 & \text{if } 2 < t \leq 4 \\ 10 & \text{if } 4 < t \leq 6 \end{cases}$. What is the fee for parking for 3.5 hours?

    • A. 4 dollars
    • B. 7 dollars
    • C. 10 dollars
    • D. 3.5 dollars
  3. 3. Given the step function $k(x) = \begin{cases} -2 & \text{if } x < -1 \\ 0 & \text{if } -1 \leq x \leq 1 \\ 2 & \text{if } x > 1 \end{cases}$. The value of $k(-1)$ is ___.

  4. 4. Which statement is true for the function $f(x) = \begin{cases} 2 & \text{if } 0 \leq x < 3 \\ 5 & \text{if } 3 \leq x < 6 \\ 1 & \text{if } 6 \leq x < 9 \end{cases}$?

    • A. $f(2) > f(4)$
    • B. $f(3) = f(6)$
    • C. $f(2.9) < f(3)$
    • D. $f(0) = f(8)$
  5. 5. A phone plan's cost $C(d)$ for $d$ gigabytes is: $C(d) = \begin{cases} 10 & \text{if } 0 < d \leq 2 \\ 15 & \text{if } 2 < d \leq 5 \\ 25 & \text{if } 5 < d \leq 10 \end{cases}$. What is the cost for 4.8 gigabytes? The cost is ___ dollars.

  6. 6. Consider the function $f(x) = \begin{cases} 2x - 1 & \text{if } x \leq 3 \\ 10 - x & \text{if } x > 3 \end{cases}$. What is the value of $f(3)$? ___

  7. 7. For the function $g(x) = \begin{cases} x^2 + 2 & \text{if } x < 1 \\ 4 - x & \text{if } x \geq 1 \end{cases}$, which statement describes the point on the graph at the boundary $x=1$?

    • A. An open circle at $(1, 3)$
    • B. A closed circle at $(1, 3)$
    • C. An open circle at $(1, 4)$
    • D. A closed circle at $(1, 4)$
  8. 8. A function is defined as $h(x) = \begin{cases} -4 & \text{if } x < -2 \\ x^2 & \text{if } -2 \leq x \leq 2 \\ 5 & \text{if } x > 2 \end{cases}$. Find the value of $h(2)$. ___

  9. 9. Which statement best describes the graph of the function $f(x) = \begin{cases} x + 2 & \text{if } x \leq 0 \\ 2 & \text{if } x > 0 \end{cases}$ at the boundary $x=0$?

    • A. The graph has a jump at $x=0$.
    • B. The graph is continuous at $x=0$.
    • C. The graph has an open circle at $(0, 2)$.
    • D. The function is undefined at $x=0$.
  10. 10. For the function $g(x) = \begin{cases} x^2 - 1 & \text{if } x < 2 \\ 2x - 1 & \text{if } x \geq 2 \end{cases}$, what is the value of $g(-3)$? ___