1.3 shifting, reflecting, and stretching graphs

Here are the graphs of some of the most commonly used functions in algebra

constant function f(x)= c

identity function f(x)= x

absolute value function f(x)=abs(x)

 square root function f(x)=√x

quadratic function f(x)=x^2

cubic function f(x)=x^3

Horizontal and Vertical Shifts:

let c be a positive real number.  Vertical and horizontal shifts in the graph of y=f(x)

are represented as follows...

vertical shift up h(x)= f(x) + c

vertical shift down h(x)=f (x) - c

horizontal shift right h(x)= f(x-c)

horizontal shift left h(x)= f(x+c)

Reflection in the coordinate axes:

reflection in the x axis h(x)= -f(x)

(this makes all the  y coordinates negative while the x coordinates stay positive, so the graph would be reflected across the x axis)

reflection in the y axis h(x)= f(-x)

(this makes all the x coordinates negative while the y coordinates stay positive, so the graph would be reflected across the y axis)

Stretching/compressing:

if the transformation of the graph y=f(x) is represented by y=cf(x)...

vertical stretch if c>1

vertical compression if 0<c<1

if the transformation is represented by y=f(cx)...

horizontal stretch if 0<c<1

horizontal compression if c>1

I think that basically covers all we need to know since this is all review.

-Megan