The image presents a graph titled "Pickup Truck Market Share" which illustrates the light vehicle market share (in percent) in a particular country for pickup trucks from 1995 to 2003. The x-axis represents the year, starting from 1995 (x = 0) to 2003 (x = 8), and the y-axis indicates the market share percentage.### Graph Details:- **Data Points**: - (0, 42.5): In 1995, the market share was 42.5%. - (4, 39.3): In 1999, the market share decreased to 39.3%. - (8, 32.8): By 2003, the market share further decreased to 32.8%.The graph consists of two line segments joining these points, indicating a downward trend in market share over the period.### Problem:(a) Use the points on the graph to write equations for the line segments in the intervals [0,4] and [4,8].- **Equation for the interval [0,4]**: - Already provided in the image: $ y = 42.5 - 0.8x $.- **Equation for the interval [4,8]**: - To be calculated using the slope formula.(b) Define this graph as a piecewise-defined function $ f(x) $.### Solution:- **For $ x \in [0,4] $**: $ y = 42.5 - 0.8x $.- **For $ x \in [4,8] $**: Calculate the equation using the points (4, 39.3) and (8, 32.8): - Slope = $ \frac{32.8 - 39.3}{8 - 4} = \frac{-6.5}{4} = -1.625 $. - Using point-slope form: $ y - 39.3 = -1.625(x - 4) $. - Simplify: $ y = -1.625x + 46.8 $.### Piecewise-Defined Function:\[ f(x) = \begin{cases} 42.5 - 0.8x & \text{if } x \in [0,4] \

Answered: Image /qna-images/answer/ff135f39-08e3-4be4-b416-2ff971bf1624.jpg

The light vehicle market share (in percent) in a particular country for pickup trucks is shown in the graph. Let x= 0 represent 1995, x= 4 represent 1999, and so on. (a) Use the points on the graph to write equations for the line segments in the intervals [0,4]and (4,8]. (b) Define this graph as a piecewise-defined function f(x). (a) The equation for the line segment in the interval [0,4] is y = 42.5 - 0.8x . (Simplify your answer. Use integers or decimals for any numbers in the expression.) The equation for the line segment in the interval (4,8] is y =I (Simplify your answer. Use integers or decimals for any numbers in the expression.) Pickup Truck Market Share 45- 43- (0, 42.5) 41- |(4, 39.3) 39- 37- 35- 33- 31- 1995 (8, 32.8 2001 1997 1999 2003 Year Percent

The light vehicle market share (in percent) in a particular country for pickup trucks is shown in the graph. Let x= 0 represent 1995, x= 4 represent 1999, and so on. (a) Use the points on the graph to write equations for the line segments in the intervals [0,4]and (4,8]. (b) Define this graph as a piecewise-defined function f(x). (a) The equation for the line segment in the interval [0,4] is y = 42.5 - 0.8x . (Simplify your answer. Use integers or decimals for any numbers in the expression.) The equation for the line segment in the interval (4,8] is y =I (Simplify your answer. Use integers or decimals for any numbers in the expression.) Pickup Truck Market Share 45- 43- (0, 42.5) 41- |(4, 39.3) 39- 37- 35- 33- 31- 1995 (8, 32.8 2001 1997 1999 2003 Year Percent

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

The image presents a graph titled "Pickup Truck Market Share" which illustrates the light vehicle market share (in percent) in a particular country for pickup trucks from 1995 to 2003. The x-axis represents the year, starting from 1995 (x = 0) to 2003 (x = 8), and the y-axis indicates the market share percentage.

### Graph Details:

- **Data Points**:
- (0, 42.5): In 1995, the market share was 42.5%.
- (4, 39.3): In 1999, the market share decreased to 39.3%.
- (8, 32.8): By 2003, the market share further decreased to 32.8%.

The graph consists of two line segments joining these points, indicating a downward trend in market share over the period.

### Problem:

(a) Use the points on the graph to write equations for the line segments in the intervals [0,4] and [4,8].

- **Equation for the interval [0,4]**:
- Already provided in the image: $ y = 42.5 - 0.8x $.

- **Equation for the interval [4,8]**:
- To be calculated using the slope formula.

(b) Define this graph as a piecewise-defined function $ f(x) $.

### Solution:

- **For $ x \in [0,4] $**:
$ y = 42.5 - 0.8x $.

- **For $ x \in [4,8] $**:
Calculate the equation using the points (4, 39.3) and (8, 32.8):
- Slope = $ \frac{32.8 - 39.3}{8 - 4} = \frac{-6.5}{4} = -1.625 $.
- Using point-slope form:
$ y - 39.3 = -1.625(x - 4) $.
- Simplify:
$ y = -1.625x + 46.8 $.

### Piecewise-Defined Function:

\[ f(x) = \begin{cases}
42.5 - 0.8x & \text{if } x \in [0,4] \

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