Lesson 1.7: Symmetry

Lesson 1.7: Symmetry

Alternative Lesson

How to Test for Symmetry about the x axis

• Test for symmetry about the x-axis: Replace y with (-y). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the x-axis. Example: Use the test for symmetry about the x-axis to determine if the graph of y - 5x² = 4 is symmetric about the x-axis.

Test for symmetry about the origin

Test for symmetry about the origin: Replace y with (-y) AND x with (-x). Simplfy the equation. If the resulting equation is equivalent to the original equation then the graph is symmetrical about the origin.

Symmetry about the line y = x

we are going to be interested in creating an equation whose graph is symmetric (about y = x) with a given graph. We do so by interchanging the x's and y's

Example: Create an equation of a graph that will be symmetric

(about y = x) with the graph of y = x³ ,

for x > or = 0.

original equation: y = x³

new equation: x = y³

solve for y: y = x^1/3 , x > or = 0

Multiple Select

Which graphs have a line of symmetry? Check all of the boxes that apply.

Multiple Select

Which graphs have a line of symmetry? Check all of the boxes that apply.

Multiple Choice

Which one of the following functions is even?

• f(x) = x⁴ + x³
• g(x) = x⁴ + x²
• h(x) = x⁵ + x³
• k(x) = x³ + x

Multiple Choice

Is the graph an even, odd, or neither function?

• Even
• Odd
• Neither

Multiple Choice

The function shown in the graph is:

• even
• odd
• neither even nor odd
• both even and odd

Multiple Choice

 $y=x^2+3x+9$  

• Even Function

• Odd Function

• Function - neither even nor odd

• Not a function

Multiple Choice

Given that  $g\left(x\right)$  is an odd function and that  $g\left(2.5\right)=4$  , which statement must also be true?

•  $g\left(-2.5\right)=-4$  

•  $g\left(2.5\right)=-4$  

•  $g\left(-2.5\right)=4$  

•  $g\left(4\right)=2.5$  

Multiple Choice

Given that  $f\left(x\right)$  is an even function and that  $f\left(-3\right)=19$  , which statement must also be true?

•  $f\left(3\right)=19$  

•  $f\left(-3\right)=-19$  

•  $f\left(3\right)=-19$  

•  $f\left(19\right)=-3$  

Multiple Choice

 $x=-2$  

• Even Function

• Odd Function

• Function - neither even nor odd

• Not a function

Multiple Choice

 $y=7$  

• Even Function

• Odd Function

• Function - neither even nor odd

• Not a function