Please help me solve with work shown ### Graphing Piecewise FunctionsIn this exercise, you are asked to graph the piecewise function \( f(x) \) defined as follows:\[ f(x) = \begin{cases} 3x - 2 & \text{if } x < 2 \\ (x - 2)^2 + 4 & \text{if } 2 \leq x < 3 \\ 5 & \text{if } x \geq 3 \end{cases} \]### Instructions:1. **Plot the function** for each segment on the coordinate plane.2. **Identify and label all intercepts** (x-intercepts and y-intercepts).### Graph Segments Explanation:- **Segment 1: \( y = 3x - 2 \)** - This linear function is defined for \( x < 2 \). - Find the intercepts: - **Y-intercept** is where \( x = 0 \): \( y = 3(0) - 2 = -2 \). - **X-intercept** is where \( y = 0 \): \( 0 = 3x - 2 \implies x = \frac{2}{3} \).- **Segment 2: \( y = (x - 2)^2 + 4 \)** - This quadratic function is defined for \( 2 \leq x < 3 \). - Since the domain starts at \( x = 2 \), you need to check the continuity: - Evaluate at \( x = 2 \): \( y = (2 - 2)^2 + 4 = 4 \). - Evaluate at \( x = 3 \): \( y = (3 - 2)^2 + 4 = 5 \).- **Segment 3: \( y = 5 \)** - This constant function is defined for \( x \geq 3 \). - It remains constant at \( y = 5 \).### Instructions for Graphing:- Use a different color or style of line (solid, dashed) for each segment to clearly differentiate between the piecewise functions.- Ensure that you include open or closed circles to mark the endpoints of each segment accurately.- Label the intercepts and any points of interest, especially transitions between the different function definitions.### Additional Notes

Name: Please help me solve with work shown ### Graphing Piecewise FunctionsI
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help me solve with work shown ### Graphing Piecewise FunctionsIn this exercise, you are asked to graph the piecewise function \( f(x) \) defined as follows:\[ f(x) = \begin{cases} 3x - 2 & \text{if } x < 2 \\ (x - 2)^2 + 4 & \text{if } 2 \leq