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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![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:
\[ f(x) = \begin{cases}
42.5 - 0.8x & \text{if } x \in [0,4] \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffddee7b2-40d8-4b5d-b201-95f80dea9273%2Fff135f39-08e3-4be4-b416-2ff971bf1624%2Fi0ilx8m_processed.png&w=3840&q=75)
Transcribed Image Text: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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