Scaling, translations, shift up / down and left/right Graphing Functions Scaling, translations, shift up / down and left/right

Linear functions y = 3x + 6 It’s x to the power of 1 So it’s a straight line And it has 1 root y = mx + c slope y- intercept….i.e. where the line cuts the x-axis

Linear Functions – real life y=12-0.5x Height of candle depends on hours burning Y=40x+60 Cost of plumber depends on hours worked Y=2x-2 Number of games in league depends on number of teams Y=3x-10 Number 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 + ??? Q1 This has a slope of 2 Also, notice where it cuts the y-axis

y = 2x + ??? Q2 This still has a slope of 2 Where does it cut the y-axis now?

y = 2x + ??? Q3 This still has a slope of 2 Where does it cut the y-axis now?

y = 2x + ??? Q4 This still has a slope of 2 Where does it cut the y-axis now?

y = 2x + ??? Q5 This still has a slope of 2 Where does it cut the y-axis now?

Linear functions with different slopes y = x + 3 This has a slope of 1 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Positive slope

Linear functions with different slopes y = 2x + 3 This has a slope of 2 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Positive slope

Linear functions with different slopes y = 3x + 3 This has a slope of 3 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Positive slope

Linear functions with different slopes y = 4x + 3 This has a slope of 4 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Positive slope

Linear functions with different slopes y = 5x + 3 This has a slope of 3 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Positive slope

Linear functions with different slopes y = x + 3 This has a slope of 1 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Positive slope

Linear functions with different slopes y = -x + 3 This has a slope of -1 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Negative slope

Linear functions with different slopes y = -2x + 3 This has a slope of -2 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Negative slope

Linear functions with different slopes y = -3x + 3 This has a slope of -3 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Negative slope

Linear functions with different slopes y = -4x + 3 This has a slope of -4 Cuts the y-axis at 3, as before Remember: Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s Negative slope

Quadratic functions y = x2

Quadratic functions y = -x2

Quadratic functions y = x2 This has a minimum point of (0,0)

Quadratic functions y = x2 +1 This has a minimum point of (0,1)

Quadratic functions y = x2 + 3 This has a minimum point of (0,3)

Quadratic functions y = x2 -2 This has a minimum point of (0,-2)

Quadratic functions y = x2 - 0.5 This has a minimum point of (0,-0.5)

Quadratic functions y = (x-1)2 This has a minimum point of (1,0)

Quadratic functions y = (x-3)2 This has a minimum point of (3,0)

Quadratic functions y = (x + 4)2 This has a minimum point of (-4,0)

Quadratic functions y = (x +1.5)2 This has a minimum point of (-1.5,0)

Quadratic functions y = (x -2)2 - 3 This has a minimum point of (2, -3)

Quadratic functions y = (x - 2)2 + 3 This has a minimum point of (2, 3)

Quadratic functions y = (x +2)2 -1 This has a minimum point of (2, -1)

Quadratic functions y = (x – 2.5)2 -0.5 This has a minimum point of (2.5, -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

Q1 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q2 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q3 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q4 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q5 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q6 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q7 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q8 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q9 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q10 Quadratic functions y = ……… This has a minimum point of …… ( , )

Q11 Quadratic functions y = ……… This has a minimum point of …… ( , )

Quadratic functions Q12 y = ……… This has a minimum point of …… ( , )

Quadratic functions Q13 y = ……… This has a minimum point of …… ( , )

Quadratic functions Q14 y = ……… This has a minimum point of …… ( , )

Quadratic functions Q15 y = ……… This has a minimum point of …… ( , )

Exponential functions y = 2x This cuts the x-axis at (1,0)

Exponential functions y = 2x +1 This cuts the x-axis at (2,0) ……. 1 higher

Exponential functions y = 2x -3 This cuts the x-axis at (-3,0)…… 3 lower

Exponential functions y = 2x This cuts the x-axis at (1,0)

Exponential functions y = 2x+1 This moves the graph 1 place to the left

Exponential functions y = 2x This cuts the x-axis at (1,0)

Exponential functions y = 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.