Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2...
Transcript of Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2...
![Page 1: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/1.jpg)
Section 3.1
Linear Functions and Their Properties
![Page 2: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/2.jpg)
![Page 3: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/3.jpg)
![Page 4: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/4.jpg)
( ) 2Graph the linear function: 13
f x x= +
−4 −3 −2 −1 1 2 3 4 5
−4
−3
−2
−1
1
2
3
4
x
y2This linear function has a slope of and3
a -intercept of 1 so first plot the point (0,1),the -intercept.yy
2Next, the slope = so change the3
value of the point on the graph by2 and the value by 3.
yx
yx
Δ
Δ
2yΔ =
3xΔ =
![Page 5: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/5.jpg)
![Page 6: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/6.jpg)
![Page 7: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/7.jpg)
![Page 8: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/8.jpg)
![Page 9: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/9.jpg)
![Page 10: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/10.jpg)
Since the average rate of change is not constant, the function is not linear.
![Page 11: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/11.jpg)
![Page 12: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/12.jpg)
![Page 13: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/13.jpg)
Since the average rate of change is a constant –0.25, the function is linear.
![Page 14: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/14.jpg)
CONSTANT
![Page 15: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/15.jpg)
![Page 16: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/16.jpg)
Determine whether the following linear functions are increasing,decreasing, or constant.(a) ( ) 2 4 (b) ( ) 5
3(c) ( ) (d) ( ) 34
f x x g x
s t t m z z
= − + =
= = −
(a) The linear function has a slope of 2 so the function is decreasing.f−
(b) This function could be written ( ) 0 5 so the function has a slope of 0 and is function is constant.
g x xg
= +
3(c) The linear function has a slope of so the function is increasing.4
s
(d) The linear function has a slope of 1 so the function is increasing.m
![Page 17: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/17.jpg)
![Page 18: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/18.jpg)
![Page 19: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/19.jpg)
Let ( ) represent the value of each car after years.V x x(0) $28,000 and the slope is 4000 since the car depreciates
by that amount per year.V = −
( ) 4000 28000V x x= − +
![Page 20: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/20.jpg)
( ) ( )3 4000 3 2800 16000V = − + =
![Page 21: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/21.jpg)
(d) The slope is the average rate of change and is –4000 so this means that for each additional year that passes, the book value of the car decreases by $4000.
(e) 8000 4000 28000x= − +
20000 4000x− = −20000 54000
x −= =−
The car will have a book value of $8000 when it is 5 years old.
![Page 22: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/22.jpg)
60 900 15 2850p p− = − +75 3750p = 50p =
( ) ( )50 60 50 900 2100s = − =
So the equilibrium price is $50 and the equilibrium quantity is 2100 phones.
![Page 23: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/23.jpg)
60 900 15 2850p p− > − +
75 3750p >
50p >
![Page 24: Section 3.1 Linear Functions and Their Properties · (a) The linear function has a slope of − 2 so the function is decreasing.f (b) This function could be written ( ) 0 5 so the](https://reader033.fdocuments.in/reader033/viewer/2022050218/5f641599255515130b7b2adc/html5/thumbnails/24.jpg)