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# Section 3 - Shifting, Reflecting, and Stretching Graphs

last edited by 14 years ago

There are 6 "parent" graphs, or commonly used graphs f(x)=C f(x)=x f(x)= |x| f(x) =  f(x) =  f(x) = Vertical Shift

g(x) = f(x) + c           (c is the vertical shift)

+ c up, - c down

Example y= - 4 Example y= +7 Horizontal Shift

g(x) = f(x + c)        horizontal shift within parenthesis,   opposite of sign

+ c moves left c

- c moves right c

Example  Example  Reflections

g(x) = -f(x)      When negative is outside, reflect over x-axis

g(x) = f(-x)      When negative is inside, reflect over y-axis  Stretch or Shrink

g(x) = cf(x)

when c is greater than or equal to 1, stretch  (steeper slope)

when c is less than 1 but c is greater than 0 (fractions), shrink  (smaller slope)

example  example   