![Page 1: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/1.jpg)
Graphing Functions
Scaling, translations, shift up / down and left/right
![Page 2: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/2.jpg)
Linear functions
y = mx + c
slope y- intercept….i.e. where the line cuts the x-axis
y = 3x + 6
• It’s x to the power of 1• So it’s a straight line• And it has 1 root
![Page 3: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/3.jpg)
Linear Functions – real lifey=12-0.5xHeight of candle depends on hours burning
Y=40x+60Cost of plumber depends
on hours worked
Y=2x-2Number of games in league depends on number of teams
Y=3x-10Number of ice creams sold
depends on temperature outside
![Page 4: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/4.jpg)
y = 2x + 3
• This has a slope of 2
• Also, notice where it cuts the y-axis
![Page 5: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/5.jpg)
y = 2x + 4
• This still has a slope of 2
• Where does it cut the y-axis now?
![Page 6: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/6.jpg)
y = 2x -3
• This still has a slope of 2
• Where does it cut the y-axis now?
![Page 7: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/7.jpg)
y = 2x + 0.5
• This still has a slope of 2
• Where does it cut the y-axis now?
![Page 8: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/8.jpg)
y = 2x
• This still has a slope of 2
• Where does it cut the y-axis now?
![Page 9: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/9.jpg)
Student Activity
For the following LINEAR graphs, complete the equation of the LINE
Just look at the y-intercept
![Page 10: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/10.jpg)
y = 2x + ???
• This has a slope of 2
• Also, notice where it cuts the y-axis
Q1
![Page 11: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/11.jpg)
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q2
![Page 12: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/12.jpg)
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q3
![Page 13: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/13.jpg)
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q4
![Page 14: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/14.jpg)
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q5
![Page 15: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/15.jpg)
Linear functions with different slopes
• This has a slope of 1
• Cuts the y-axis at 3, as before
y = x + 3
Remember:
Slope = =
Positive slope
![Page 16: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/16.jpg)
Linear functions with different slopes
• This has a slope of 2
• Cuts the y-axis at 3, as before
y = 2x + 3
Remember:
Slope = =
Positive slope
![Page 17: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/17.jpg)
Linear functions with different slopes
• This has a slope of 3
• Cuts the y-axis at 3, as before
y = 3x + 3
Remember:
Slope = =
Positive slope
![Page 18: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/18.jpg)
Linear functions with different slopes
• This has a slope of 4
• Cuts the y-axis at 3, as before
y = 4x + 3
Remember:
Slope = =
Positive slope
![Page 19: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/19.jpg)
Linear functions with different slopes
• This has a slope of 3
• Cuts the y-axis at 3, as before
y = 5x + 3
Remember:
Slope = =
Positive slope
![Page 20: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/20.jpg)
Linear functions with different slopes
• This has a slope of 1
• Cuts the y-axis at 3, as before
y = x + 3
Remember:
Slope = =
Positive slope
![Page 21: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/21.jpg)
Linear functions with different slopes
• This has a slope of -1
• Cuts the y-axis at 3, as before
y = -x + 3
Remember:
Slope = =
Negative slope
![Page 22: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/22.jpg)
Linear functions with different slopes
• This has a slope of -2
• Cuts the y-axis at 3, as before
y = -2x + 3
Remember:
Slope = =
Negative slope
![Page 23: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/23.jpg)
Linear functions with different slopes
• This has a slope of -3
• Cuts the y-axis at 3, as before
y = -3x + 3
Remember:
Slope = =
Negative slope
![Page 24: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/24.jpg)
Linear functions with different slopes
• This has a slope of -4
• Cuts the y-axis at 3, as before
y = -4x + 3
Remember:
Slope = =
Negative slope
![Page 25: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/25.jpg)
Quadratic functions
y = x2
![Page 26: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/26.jpg)
Quadratic functions
y = -x2
![Page 27: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/27.jpg)
Quadratic functions
• This has a minimum point of (0,0)
y = x2
![Page 28: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/28.jpg)
Quadratic functions
• This has a minimum point of (0,1)
y = x2 +1
![Page 29: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/29.jpg)
Quadratic functions
• This has a minimum point of (0,3)
y = x2 + 3
![Page 30: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/30.jpg)
Quadratic functions
• This has a minimum point of (0,-2)
y = x2 -2
![Page 31: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/31.jpg)
Quadratic functions
• This has a minimum point of (0,-0.5)
y = x2 - 0.5
![Page 32: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/32.jpg)
Quadratic functions
• This has a minimum point of (1,0)
y = (x-1)2
![Page 33: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/33.jpg)
Quadratic functions
• This has a minimum point of (3,0)
y = (x-3)2
![Page 34: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/34.jpg)
Quadratic functions
• This has a minimum point of (-4,0)
y = (x + 4)2
![Page 35: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/35.jpg)
Quadratic functions
• This has a minimum point of (-1.5,0)
y = (x +1.5)2
![Page 36: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/36.jpg)
Quadratic functions
• This has a minimum point of (2, -3)
y = (x -2)2 - 3
![Page 37: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/37.jpg)
Quadratic functions
• This has a minimum point of (2, 3)
y = (x - 2)2 + 3
![Page 38: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/38.jpg)
Quadratic functions
• This has a minimum point of (2, -1)
y = (x +2)2 -1
![Page 39: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/39.jpg)
Quadratic functions
• This has a minimum point of (2.5, -0.5)
y = (x – 2.5)2 -0.5
![Page 40: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/40.jpg)
Student Activity
For the following quadratic graphs write down the equation of the curve
Just figure out how much it has moved up or down from the x-axis
And how much it has moved left or right from the origin
![Page 41: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/41.jpg)
Quadratic functions
• This has a minimum point of …… ( , )
y = ………
Q1
![Page 42: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/42.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q2
![Page 43: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/43.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q3
![Page 44: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/44.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q4
![Page 45: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/45.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q5
![Page 46: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/46.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q6
![Page 47: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/47.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q7
![Page 48: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/48.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q8
![Page 49: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/49.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q9
![Page 50: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/50.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q10
![Page 51: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/51.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q11
![Page 52: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/52.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q12
![Page 53: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/53.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q13
![Page 54: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/54.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q14
![Page 55: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/55.jpg)
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q15
![Page 56: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/56.jpg)
Exponential functionsy = 2x
• This cuts the x-axis at (1,0)
![Page 57: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/57.jpg)
Exponential functionsy = 2x +1
• This cuts the x-axis at (2,0) ……. 1 higher
![Page 58: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/58.jpg)
Exponential functionsy = 2x -3
• This cuts the x-axis at (-3,0)…… 3 lower
![Page 59: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/59.jpg)
Exponential functionsy = 2x
• This cuts the x-axis at (1,0)
![Page 60: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/60.jpg)
Exponential functionsy = 2x+1
• This moves the graph 1 place to the left
![Page 61: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/61.jpg)
Exponential functionsy = 2x
• This cuts the x-axis at (1,0)
![Page 62: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/62.jpg)
Exponential functionsy = 2x-3
• This moves the graph 3 places to the right
![Page 63: Graphing Functions Scaling, translations, shift up / down and left/right](https://reader036.vdocuments.us/reader036/viewer/2022062301/56649f285503460f94c40054/html5/thumbnails/63.jpg)
• See modular course worksheet – guessing which graph is which and what translation has happened to it.