1.2 day 2 webstaffweb.psdschools.org/kemotich/mrs_motichka/precalculus...1.2 day 2 graphs of...
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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)
Graphically
Find the intercepts of the following function.
Algebraically
Find xintercept: let y = 0 and solve for x
Find yintercept: let x = 0 and solve for y
x y
Title: Sep 5 9:48 PM (2 of 10)
Graphically Algebraically
Find xintercept: let y = 0 and solve for x
Find yintercept: let x = 0 and solve for y
Find the intercepts of the following function.
x y
Title: Sep 5 9:48 PM (3 of 10)
The same shape or measure on either side of a line or point; a reflection, a mirror image
What is Symmetry?
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
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 .)
Test for symmetry.
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)