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Section 3 - Shifting, Reflecting, and Stretching Graphs

Page history last edited by PBworks 14 years ago

 

 

There are 6 "parent" graphs, or commonly used graphs

 

 

 

 

                                     f(x)=C

 

 

 

 

 

 

 

 

                                 f(x)=x

 

 

 

 

 

 

 

                       f(x)= |x|

 

 

 

 

                             f(x) = eq=\sqrt{x}

 

 

 

                                f(x) = eq=x^2

 

 

 

 

                        f(x) = eq=x^3

 

 

 

Vertical Shift

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

+ c up, - c down

 

Example y= eq=x^2  - 4

  

 

 

Example y= eq=x^2  +7

 

 

 

 Horizontal Shift

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

+ c moves left c

- c moves right c

 

Example eq=y=(x-3)^2

 

 

 

 

 

Example eq=y=(x+2)^2+6

 

 

 

 

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

 

 

 

 

        eq=y=-\sqrt{x}

 

 

 

 

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

eq=y=3x^2

 

 

 

 

 

 

example

eq=y=\frac{1}{4}x^2

Comments (1)

Anonymous said

at 8:20 pm on Jan 8, 2008

Graphs were major in this section - what happened to them? Also, check out the options for formatting with exponents. 15/20

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