Graph this function.
f(x)=
–
1/2
x–3	if x<2
4x–6	if x≥2
Select points

The function \( f(x) \) is a piecewise function:

\[
f(x) =
\begin{cases}
-\frac{1}{2}x - 3 & \text{if } x < 2 \\
4x - 6 & \text{if } x \geq 2
\end{cases}
\]

### Steps to graph this function:

1. **For \( x < 2 \):**  
   The equation is \( f(x) = -\frac{1}{2}x - 3 \).  
   This represents a line with a slope of \( -\frac{1}{2} \) and a y-intercept of \( -3 \).  
   We can calculate a few points for this part:
   - At \( x = 0 \), \( f(0) = -\frac{1}{2}(0) - 3 = -3 \).  
   - At \( x = 1 \), \( f(1) = -\frac{1}{2}(1) - 3 = -3.5 \).  
   - At \( x = -1 \), \( f(-1) = -\frac{1}{2}(-1) - 3 = -2.5 \).

2. **For \( x \geq 2 \):**  
   The equation is \( f(x) = 4x - 6 \).  
   This represents a line with a slope of \( 4 \) and a y-intercept of \( -6 \).  
   We can calculate a few points for this part:
   - At \( x = 2 \), \( f(2) = 4(2) - 6 = 2 \).  
   - At \( x = 3 \), \( f(3) = 4(3) - 6 = 6 \).  
   - At \( x = 4 \), \( f(4) = 4(4) - 6 = 10 \).

### Important Notes:
- The function has a **break** at \( x = 2 \), where it changes from one equation to another. At this point, we use the second equation to find \( f(2) = 2 \).
- The graph should show a **line segment** for \( x < 2 \) and a **line segment** for \( x \geq 2 \), with a **filled circle** at \( x = 2 \) because the function is defined at \( x = 2 \) (it uses the second equation).

Would you like to visualize this graph?

Graph this function. f(x) = -1/2 x - 3 if x < 2, 4x - 6 if x ≥ 2

Learn how to graph the piecewise function f(x) = -1/2x - 3 for x < 2 and f(x) = 4x - 6 for x ≥ 2. This problem involves graphing two linear functions with a break at x = 2, and is suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation