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.