For the function piece defined by $f(x) = 2x + 1$ for $x > 3$, which type of circle should be used on its graph at the boundary $x=3$?

Both an open and a closed circle

A function is defined as $h(x) = x^2 + 1$ for $x < -2$ and $h(x) = 3 - x$ for $x \geq -2$. What points and circle types are used at the boundary $x = -2$?

Open circle at $(-2, 5)$ and closed circle at $(-2, 5)$

Open circle at $(-2, 1)$ and closed circle at $(-2, 5)$

Closed circle at $(-2, 5)$ and open circle at $(-2, 1)$

Open circle at $(-2, 5)$ and open circle at $(-2, 1)$

Piecewise Functions Practice — Grade 8 math

Lesson 7: Piecewise Functions — Practice Questions

1. For the function piece defined by $f(x) = 2x + 1$ for $x > 3$, which type of circle should be used on its graph at the boundary $x=3$?
- A. An open circle
- B. A closed circle
- C. Both an open and a closed circle
- D. No circle is needed
2. A function is defined as $h(x) = x^2 + 1$ for $x < -2$ and $h(x) = 3 - x$ for $x \geq -2$. What points and circle types are used at the boundary $x = -2$?
- A. Open circle at $(-2, 5)$ and closed circle at $(-2, 5)$
- B. Open circle at $(-2, 1)$ and closed circle at $(-2, 5)$
- C. Closed circle at $(-2, 5)$ and open circle at $(-2, 1)$
- D. Open circle at $(-2, 5)$ and open circle at $(-2, 1)$
3. The graph of a piece of a piecewise function has a closed circle at its boundary point $(4, 10)$. Which inequality could define the domain for this piece?
- A. $x > 4$
- B. $x < 4$
- C. $x \geq 4$
- D. $x \neq 4$
4. 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 $f(3)$? ___
5. 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 $(1, 4)$
6. 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 $h(2)$. ___
7. 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 $x=0$.
8. 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 $g(-3)$? ___