Symmetry
•
X – axis symmetry
– Algebraically
• If you plug in –y and simplify the equation and it is the exact same as before then it is
symmetric
– Graphically
• It is a reflection over the x axis
•
Y – axis symmetry
– Algebraically
• If you plug in – x and simplify the equation and it is the exact same as before then it is
symmetric
– Graphically
• It is a reflection over the y axis
•
Origin Symmetry
– Algebraically
• If you plug in – x and – y and simplify the equation and it is the exact same as before
then it is symmetric
– Graphically
• Your graph can rotate 180 degrees and be the same.
Find the intercepts of the following
graphs and determine if it has
symmetry.
Finish the graph so it has the
symmetry indicated.
Find the intercepts and test for
symmetry.
y  3x
Find the intercepts and test for
symmetry.
x  y 4
2
Find the intercepts and test for
symmetry.
x  y 9
2
2
Find the intercepts and test for
symmetry.
y4 x
Determine if the relation is a
function, then for each function
state the domain and range.
• {(2, 6), (-3, 6), (4, 9), (2, 10)}
• {(-2, 4), (-2, 6), (0,3), (3, 7)}
Find the following values for f(x)=3x2+2x – 4
f(0)
f(1)
f(-1)
f(-x)
-f(x)
f(x+1)
f(2x)
f(x+h)
Find the following values for f(x)=(2x+1)/(3x-5)
f(0)
f(1)
f(-1)
f(-x)
-f(x)
f(x+1)
f(2x)
f(x+h)
Find the Domain
x
g ( x)  2
x  16
Find the Domain
g ( x)  5x  4
Find f+g, f – g, f*g, f/g and state the
domain of each
f ( x)  3 x  4
g ( x)  2 x  3
Find f+g, f – g, f*g, f/g and state the
domain of each
f ( x)  x
g ( x)  3 x  5