Chapter 4: Transformations of Functions

Question 1

Translations (horizontal and vertical)

Answer 1

Horizontal: f(x) –> f(x-a)
- Moved horizontally by a units
(If a>0, eg. f(x-3), graph is translated to the right by 3 units)
(If a<0, eg. f(x+3), graph is translated to the left by 3 units)

Vertical: f(x) –> f(x) + b
- Moved vertically by b units
(If b>0, b is translated upwards by b units)
(If b<0, b is translated downwards by b units)

Horizontal AND Vertical translation: f(x-a) +b
- Expressed as translated by the vector (a,b)

Question 2

Stretch (horizontal and vertical)

Answer 2

Vertical: f(x) –> pf(x)
- If p>0, graph moves p-times its previous distance away from the x-axis
- If 0<p<1, graph moves p-times its previous distance towards the x-axis

Horizontal: f(x) –> f(qx)
- If q>0, point moves 1/q times closer to the y-axis
- If 0<q<1, point moves 1/q times further from the y-axis

Question 3

Reflection (at x-axis and y-axis)

Answer 3

At y-axis: f(x) –> - f(x)
- y-coordinate changes sign
- x-coordinate remains the same

At x-axis: f(x) –> f(-x)
- x-coordinate changes sign
- y-coordinate remains the same