Graph transformations: reflections

The Maths Habit Handout to print

Raise your right hand in front of a mirror. Which hand does your reflection seem to raise?

The left: left and right swap, up and down do not

Reflection
A flip in a mirror line.

−f(x)reflect in the x-axis f(−x)reflect in the y-axis

Which axis is the mirror line?

y = −f(x) The x-axis

Sketch y = −f(x).

The graph is reflected in the
x-axisy-axis
P goes to
(4,−1)

Sketch y = −f(x).

The graph is reflected in the
x-axisy-axis
P goes to
(−4,1)

Sketch y = −f(x).

The graph is reflected in the
x-axisy-axis
P goes to
(4,−1)

Sketch y = −f(x).

The graph is reflected in the
x-axisy-axis
P goes to
(−1,−2)

Which axis is the mirror line?

y = f(−x) The y-axis

Sketch y = f(−x).

The graph is reflected in the
x-axisy-axis
P goes to
(−4,1)

Sketch y = f(−x).

The graph is reflected in the
x-axisy-axis
P goes to
(4,−1)

Sketch y = f(−x).

The graph is reflected in the
x-axisy-axis
P goes to
(−4,1)

Sketch y = f(−x).

The graph is reflected in the
x-axisy-axis
P goes to
(−3,2)

Graph transformations: reflections worksheet, page 1

Graph transformations: reflections worksheet, page 2

Answer sheet

  1. The graph of y = f(x) is reflected to give y = −f(x). Which points on the graph do not move?

    Points on the x-axis

  2. The graph of y = x2 − 4x is reflected in the y-axis. Write its new equation.

    y = x2 + 4x

  1. The graph of y = f(x) is drawn. Sketch y = −f(x).

    Reflected in the x axis
    xy−3−2−10123−3−2−10123

  2. P(−5, 4) is on y = f(x). Where is P on y = f(−x)?

    (5, 4)

  3. The graph of y = x2 − 2x + 5 is reflected in the y axis. Write the equation of the new graph.

    y = x2 + 2x + 5
Exit tickets to print