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)