graphing functions scaling, translations, shift up / down and left/right
TRANSCRIPT
Graphing Functions
Scaling, translations, shift up / down and left/right
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
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
y = 2x + 3
• This has a slope of 2
• Also, notice where it cuts the y-axis
y = 2x + 4
• This still has a slope of 2
• Where does it cut the y-axis now?
y = 2x -3
• This still has a slope of 2
• Where does it cut the y-axis now?
y = 2x + 0.5
• This still has a slope of 2
• Where does it cut the y-axis now?
y = 2x
• This still has a slope of 2
• Where does it cut the y-axis now?
Student Activity
For the following LINEAR graphs, complete the equation of the LINE
Just look at the y-intercept
y = 2x + ???
• This has a slope of 2
• Also, notice where it cuts the y-axis
Q1
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q2
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q3
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q4
y = 2x + ???
• This still has a slope of 2
• Where does it cut the y-axis now?
Q5
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
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
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
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
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
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
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
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
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
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
Quadratic functions
y = x2
Quadratic functions
y = -x2
Quadratic functions
• This has a minimum point of (0,0)
y = x2
Quadratic functions
• This has a minimum point of (0,1)
y = x2 +1
Quadratic functions
• This has a minimum point of (0,3)
y = x2 + 3
Quadratic functions
• This has a minimum point of (0,-2)
y = x2 -2
Quadratic functions
• This has a minimum point of (0,-0.5)
y = x2 - 0.5
Quadratic functions
• This has a minimum point of (1,0)
y = (x-1)2
Quadratic functions
• This has a minimum point of (3,0)
y = (x-3)2
Quadratic functions
• This has a minimum point of (-4,0)
y = (x + 4)2
Quadratic functions
• This has a minimum point of (-1.5,0)
y = (x +1.5)2
Quadratic functions
• This has a minimum point of (2, -3)
y = (x -2)2 - 3
Quadratic functions
• This has a minimum point of (2, 3)
y = (x - 2)2 + 3
Quadratic functions
• This has a minimum point of (2, -1)
y = (x +2)2 -1
Quadratic functions
• This has a minimum point of (2.5, -0.5)
y = (x – 2.5)2 -0.5
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
Quadratic functions
• This has a minimum point of …… ( , )
y = ………
Q1
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q2
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q3
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q4
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q5
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q6
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q7
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q8
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q9
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q10
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q11
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q12
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q13
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q14
Quadratic functionsy = ………
• This has a minimum point of …… ( , )
Q15
Exponential functionsy = 2x
• This cuts the x-axis at (1,0)
Exponential functionsy = 2x +1
• This cuts the x-axis at (2,0) ……. 1 higher
Exponential functionsy = 2x -3
• This cuts the x-axis at (-3,0)…… 3 lower
Exponential functionsy = 2x
• This cuts the x-axis at (1,0)
Exponential functionsy = 2x+1
• This moves the graph 1 place to the left
Exponential functionsy = 2x
• This cuts the x-axis at (1,0)
Exponential functionsy = 2x-3
• This moves the graph 3 places to the right
• See modular course worksheet – guessing which graph is which and what translation has happened to it.