The image presents a task to graph a piecewise function defined as follows:\[ h(x) = \begin{cases} 2x & \text{if } 0 \leq x \leq 30 \\x - 30 & \text{if } 30 < x \leq 50 \\0.5x + 65 & \text{if } x > 50 \end{cases}\]Below the function definition, there is an instruction: "Choose the correct graph below."There are four graph options labeled A, B, C, and D, each representing different line segments that supposedly correspond to the given piecewise function. Each option shows a graph with:- The x-axis labeled from 0 to 75 at intervals of 15.- The y-axis labeled from 0 to 105 at intervals of 15.- Grids are evenly spaced for both axes.- Graphs contain line segments with various slopes and intersections, visually representing the segments of the piecewise function.Each graph has three sections:1. A linear segment for $0 \leq x \leq 30$2. A linear segment for $30 < x \leq 50$3. A linear segment for $x > 50$The task is to identify which graph accurately reflects these segments according to the defined piecewise function.

Answered: Image /qna-images/answer/42b01e0f-e6b9-4832-be34-dfffbf3b60c0.jpg

Answered: Graph the function hoo-x-30 0x30 30x50…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

The image presents a task to graph a piecewise function defined as follows:

\[
h(x) =
\begin{cases}
2x & \text{if } 0 \leq x \leq 30 \\
x - 30 & \text{if } 30 < x \leq 50 \\
0.5x + 65 & \text{if } x > 50
\end{cases}
\]

Below the function definition, there is an instruction:

"Choose the correct graph below."

There are four graph options labeled A, B, C, and D, each representing different line segments that supposedly correspond to the given piecewise function.

Each option shows a graph with:

- The x-axis labeled from 0 to 75 at intervals of 15.
- The y-axis labeled from 0 to 105 at intervals of 15.
- Grids are evenly spaced for both axes.
- Graphs contain line segments with various slopes and intersections, visually representing the segments of the piecewise function.

Each graph has three sections:

1. A linear segment for $0 \leq x \leq 30$
2. A linear segment for $30 < x \leq 50$
3. A linear segment for $x > 50$

The task is to identify which graph accurately reflects these segments according to the defined piecewise function.

Expert Solution

Step 1: Given

$f open parentheses x close parentheses equals open curly brackets table row cell 2 x space space space space space space space space space space space space space space space i f space 0 less or equal than x less or equal than 30 end cell row cell x plus 30 space space space space space space space space space space i f space 30 less than x less or equal than 50 end cell row cell 0.5 x space plus space 65 space space i f space x greater than 50 end cell end table close$