Shifting, Reflecting, and Stretching Graphs

In order to to help with shifting, reflecting, and stretching graphs, it is important to know and understand the graphs below.

f(x)=x

f(x)=sqrt{x}

f(x)=x^2

f(x)=|x|

Graphs can be shifted horizontally and vertically using these rules:

h(x)=f(x)+k means a shift up k units

h(x)=f(x)-k means a shift down k units

h(x)=f(x+k) means a shift left k units

h(x)=f(x-k) means a shift right k units

when k is greater than or equal to 0. 

Graphs can be reflected using these rules

h(x)= -f(x) means reflection across the x-axis

h(x)= f(-x) means a reflection across the y axis

Graphs can be stretched and condensed using these rules

h(x)= c*f(x) when c>1 means  it is condensed

h(x)= c*f(x) when c<1 means it is stretched