Rules For Transformation Of Linear Functions

Question 1

Horizontal shift

Answer 1

f(x+h) shift left h units

f(x-h) shift right h units

f(x)=a(x-h)^2+k

Question 2

Vertical shift

Answer 2

f(x)+k shift up k units

f(x)-k shift down k units

f(x)=a(x-h)^2+k

Question 3

Reflection

Answer 3

-f(x) reflects across the x-axis

f(-x) reflects across the y-axis

f(x)=a(x-h)^2+k

Question 4

Vertical stretch / compress

Answer 4

a f(x) when a>1:
Stretches the graph vertically by a factor of a

a f(x) when 0<a></a>

Question 5

Horizontal stretch / compress

Answer 5

f(ax) when a>1:
Compresses horizontally by a factor of 1/a

f(ax) when 0<a></a>

Question 6

What does each variable tell us about the functions graph?

y = a (x-h)^2 +k

Answer 6

a - vertical stretch or compress. Positive opens up, negative opens down.

h - horizontal shift. Negative moves right, positive moves left.

k - vertical shift. Positive moves up, negative moves down.