1.2 day 2 Graphs of Equations in Two Variables
Objective: You will be able to:
• Find the intercepts of a function.
• Test equations for symmetry with respect to the x­axis, y­axis & the origin.
Title: Sep 5 ­ 9:45 PM (1 of 10)
Find the intercepts of the following function.
Algebraically
Graphically
Find x­intercept: let y = 0 and solve for x
Find y­intercept: let x = 0 and solve for y
x
Title: Sep 5 ­ 9:48 PM (2 of 10)
y
Find the intercepts of the following function.
Algebraically
Graphically
Find x­intercept: let y = 0 and solve for x
Find y­intercept: let x = 0 and solve for y
x
Title: Sep 5 ­ 9:48 PM (3 of 10)
y
What is Symmetry?
The same shape or measure on either side of a line or point; a reflection, a mirror image
Title: Sep 5 ­ 9:14 PM (4 of 10)
A graph is symmetric with respect to the x­axis if, for every point (x , y) on the graph, the point (x , ­ y) is also on the graph.
• (x,y)
(x,-y)
Plot the following points and then plot the
point that is symmetric with respect to the
x-axis:
(3,5)
(-2,4)
(5,-2)
Title: Sep 5 ­ 9:14 PM (5 of 10)
A graph is symmetric with respect to the y­axis if, for every point (x , y) on the graph, the point (­ x , y) is also on the graph.
• (x,y)
(- x,y)
Plot the following points and then plot the
point that is symmetric with respect to the
y-axis:
(-3,5)
(2,-4)
(-1,-3)
Title: Sep 5 ­ 9:14 PM (6 of 10)
A graph is symmetric with respect to the origin if, for every point (x , y) on the graph, the point (­ x , ­ y) is also on the graph.
• (x,y)
(- x,- y)
Plot the following points and then plot the
point that is symmetric with respect to the
origin:
(2,2)
(4,-1)
(-5,3)
Title: Sep 5 ­ 9:14 PM (7 of 10)
Testing an Equation for Symmetry
Test
for symmetry.
Step 1:
Test for x-axis symmetry. (Replace y with - y,
and an equivalent equation should result.)
Step 2:
Test for y-axis symmetry. (Replace x with - x,
and an equivalent equation should result .)
Step 3:
Test for symmetry about the origin.
(Replace x with - x, and y with - y, and
an equivalent equation should result .)
Title: Sep 5 ­ 10:23 PM (8 of 10)
Testing an Equation for Symmetry
Test
for symmetry.
Step 1:
Test for x-axis symmetry. (Replace y with - y)
Step 2:
Test for y-axis symmetry. (Replace x with - x)
Step 3:
Test for symmetry about the origin.
(Replace x with - x and y with - y)
Title: Sep 5 ­ 10:23 PM (9 of 10)
Homework
1.2 day 2 p.23 #59 ­ 71, 79 ­ 82
Title: Sep 2 ­ 3:17 PM (10 of 10)