College Algebra & Trigonometry, 2018a

4.4. TRANSFORMATIONS 201
4.4 Transformations
There are three major types of transformation that we will consider:
1) Horizontal and vertical shifts
2) Reflections over the x or y-axis
3) Horizontal and vertical stretches
If we take a given function, let’s say f(x) =x, then this has the graph we see
below - a straight line with a slope of 1 and a y-intercept of 0. If we add to the
function f(x)+6=x +6, then this will add 6 to all of the y-values which shifts
the graph 6 places up.
f(x) =x g(x) =f(x)+6=x +6
8
6
4
2
−8 −6 −4 −2
−2
2 4 6 8
−4
−6
−8
8
6
4
2
−8 −6 −4 −2
−2
2 4 6 8
−4
−6
−8