Reflection in the y-axis and translation - order matters | IB Maths AI HL | Tope Teaches Maths

Compare a horizontal reflection and translation in both orders.

A reflection in the -axis changes the sign of each current -coordinate.
If a horizontal translation happens first, the reflection reverses its direction too.

Example 1

Reflect, then translate

Reflect in the -axis, then translate 3 right.

1.Reflect in the -axis.
2.Translate by .

The result is . The image of B(0, 0) is B(3, 0).

Example 2

Translate, then reflect

Translate 3 right, then reflect in the -axis.

1.Translate by .
2.Reflect in the -axis.

The result is . The image of B(0, 0) is B(−3, 0).

Remember
Substitute − into the whole current function when reflecting in the -axis. Do not change only part of the input.

Your turn

5 practice questions

Question 1

Starting with , Reflect in the -axis. Then translate by . Write the resulting function and the image of . Repeat with the order reversed.

Check answer

Given order:

,

.Reversed order:

,

.

Apply every new operation to the whole current graph. A stretch or reflection also changes any translation already made in that direction.

Question 2

Starting with , Reflect in the -axis. Then translate by . Write the resulting function and the image of . Repeat with the order reversed.

Check answer

Given order:

,

.Reversed order:

,

.

Apply every new operation to the whole current graph. A stretch or reflection also changes any translation already made in that direction.

Question 3

Starting with , Reflect in the -axis. Then translate by . Write the resulting function and the image of . Repeat with the order reversed.

Check answer

Given order:

,

.Reversed order:

,

.

Apply every new operation to the whole current graph. A stretch or reflection also changes any translation already made in that direction.

Question 4

Starting with , Reflect in the -axis. Then translate by . Write the resulting function and the image of . Repeat with the order reversed.

Check answer

Given order:

,

.Reversed order:

,

.

Apply every new operation to the whole current graph. A stretch or reflection also changes any translation already made in that direction.

Question 5

Starting with , Reflect in the -axis. Then translate by . Write the resulting function and the image of . Repeat with the order reversed.

Check answer

Given order:

,

.Reversed order:

,

.

Apply every new operation to the whole current graph. A stretch or reflection also changes any translation already made in that direction.

← All Functions cards Report a mistake