Graphs Transformations

Identify the graph, each is a quadratic with single x2 y y 25 Starter 1 identify each graph Identify the graph, each is a quadratic with single x2 y y 25 -8 8 x 5 10 x -64 Each is a quadratic with single x2 y y 5-10 mins discuss answers with students 18 -7 x -5 2 9 x

Identify the graph, each is a quadratic with single x2 y 16 y Starter 2 identify each graph Identify the graph, each is a quadratic with single x2 y 16 y -4 4 x 10 x Each is a quadratic with single x2 y y 31 5-10 mins discuss answers with students 36 6 x -5 -4 x 9

C1: Graphs 1a Starter: KUS objectives BAT know and use the six types of transformations to graphs Starter:

y = f(x) is any function or equation of a graph. Introduction y = f(x) is any function or equation of a graph. This example is a cubic function/equation. y = f(x) There are six basic types of transformation of a graph i.e. six ways we can move the graph or change its shape

Point (x, y) becomes point (x, y+a) Transf 1 y = f(x) + a y = f(x) +a Point (x, y) becomes point (x, y+a) y = f(x) + a This is a ‘shift’ in the y-direction

Point (x, y) becomes point (x-a, y) Transf 2 y = f(x) y = f(x+a) -a Point (x, y) becomes point (x-a, y) y = f(x+a) This is a ‘shift’ in the x-direction, opposite to the sign of number a

Draw a sketch graph of 𝒚= 𝒙−𝟑 𝟐 +𝟐 WB 1 Draw a sketch graph of 𝒚= 𝒙−𝟑 𝟐 +𝟐 Include any intersections and The minimum point

Include the image of points A and B WB 2 Draw a sketch graph of 𝒇 𝒙+𝟒 −𝟐 Include the image of points A and B B (4, 0) A (-2, 8) 𝒇 𝒙

Notice what happens at the zeros Transf 3 y = Af(x) y = f(x) Notice what happens at the zeros y = Af(x) This is a ‘stretch’ in the y-direction, Scale factor A. Every answer (y-coordinate) gets multiplied by A

Notice what happens at the y-intercept y = f(Ax) Transf 4 Notice what happens at the y-intercept y = f(Ax) y = f(x) y = f(Ax) This is a ‘stretch’ in the x-direction, Scale factor 1/A Every x coordinate gets multiplied by 1/A, y values stay the same

Include the image of points A and B WB 3 Draw a sketch graph of 𝒇 𝟑𝒙 Include the image of points A and B B (6, 0) A (-3, 9) 𝒇 𝒙

Include the image of points A, B and C WB 4 Draw a sketch graph of 𝟐𝒇 𝒙 Include the image of points A, B and C C (4,-2) A (-5, 7) 𝒇 𝒙 B (0, 3)

This is a ‘reflection’ in the axis, mirror line y = 0 Transf 5 y = f(x) y = -f(x) y = -f(x) This is a ‘reflection’ in the axis, mirror line y = 0 Every y coordinate gets multiplied by -1

Notice what happens at the y-intercept y = f(-x) Transf 6 Notice what happens at the y-intercept y = f(-x) y = f(x) y = f(-x) This is a ‘reflection’ in the y-axis, Every x value gets multiplied by -1, So y values are swapped around

Include the image of points A, B and C WB 5 Draw a sketch graph of 𝒇 −𝒙 Include the image of points A, B and C B (3, 5) A (-4, -2) 𝒇 𝒙 C (9, 0)

Describe these transformations WB 6 Describe these transformations a) −𝒇 𝒙 b) 𝒇 𝒙 +𝟒 c) 𝒇 𝟐𝒙 d) 𝟑𝒇 𝒙 +𝟏

Work out the equations of the transformed graphs WB 7 if 𝒇 𝒙 =𝟐 𝒙 𝟑 Work out the equations of the transformed graphs a) −𝒇 𝒙 a) −𝒇 𝒙 = -𝟐 𝒙 𝟑 b) 𝒇 𝒙 +𝟒 b) 𝒇 𝒙 +𝟒= 𝟐 𝒙 𝟑 +𝟒 c) 𝒇 𝟐𝒙 c) 𝒇 𝟐𝒙 = 𝟐 (𝟐𝒙) 𝟑 =𝟏𝟔 𝒙 𝟑 d) 𝟑𝒇 𝒙 +𝟏 d) 𝟑𝒇 𝒙 +𝟏=𝟑 𝟐𝒙 𝟑 +𝟏= 𝟔𝒙 𝟑 +𝟏

One thing to improve is – KUS objectives BAT know and use the six types of transformations to graphs self-assess One thing learned is – One thing to improve is –

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