**Transformation of Graphs**

Starter

Activity

Complete the transformations of graphs sheet.

Transforming graphs

The picture shows the graph of y = 2

**L.O. -Understand how transforming a graph effects the equation, and write equations of transformed graphs.**

x

On the same

axes sketch the graph of

(a) y = 2 - 1

(b) y = 2

x

x-1

Transforming graphs

The picture shows the graph of y = 2

x

On the same

axes sketch the graph of

(a) y = 2 - 1

(b) y = 2

x

x-1

Transforming graphs

The picture shows the graph of y = 2

x

On the same axes sketch the graph of (a) y = -2 (b) y = 2

x

-x

Transforming graphs

The picture shows the graph of y = 2

x

On the same axes sketch the graph of (a) y = -2 (b) y = 2

x

-x

Transformation of Graphs

Given the graph y = f(x)

(a) y = f(x) + a results in translation

(b) y = f(x + a) results in translation

(c) y = -f(x) results in reflection in y = 0

(d) y = f(-x) results in reflection in x = 0

0

a

-a

0

Activity

y = f(x) + 2: translation 2 up [crosses x-axis at (0,0) and (1,0)]

y = -f(x): reflection in x-axis [crosses x-axis at (-1,0) and (2,0) & y-axis at (0,2)]

y = f(x-1): translation 1 right [crosses x-axis at (0,0) and (3,0)]

y = f(x+1): translation 1 left [crosses x-axis at (-2,0) and (1,0) & y-axis at (0,-2)]

y = -f(x+1): translation 1 left then reflect in x-axis [crosses x-axis at (-2,0) and

(1,0) & y-axis at (0,2)]

y = f(-x): reflection in y-axis [crosses x-axis at (-2,0) and (1,0) & y-axis at (0,-2)]

y = f(x-1)+2: translation 1 right and 2 up [crosses x-axis (1,0) and (2,0) &

y-axis at (0,2)]

Top left: y = 1 + sin x

Top right: y = sin (x - 90)

Bottom left: either y = sin (-x) or y = - sin x

Bottom right: either sin (x+90) or y = -sin (x - 90)

The picture shows the coordinate (1,2).

Give the coordinate when the point is

(a) translated

(b) reflected in the line x = 0

(c) translated

(d) reflected in the line y = 0.

-1

0

0

-1

Starter

The picture shows the coordinate (1,2).

Give the coordinate when the point is

(a) translated

(b) reflected in the line x = 0

(c) translated

(d) reflected in the line y = 0.

-1

0

0

-1

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