AIM: What is symmetry? What are even and odd functions? Do Now : Find the x and y intercepts 1)y = x² + 3x 2) x = y² - 4 (3x + 1)² HW #3 – page 9 (#11-17, 21-25) (odd)

Look at these graphs – what kind of symmetry does it have? Symmetry with the: 1)X- Axis 2)Y- Axis 3)Origin

How would you finish this graph for symmetry with the y-axis, x-axis and the origin?

1) Symmetric with the y – axis – ▪ (x,y) and (-x,y) are points on the graph ▪ mirror image on either side of the y-axis ▪ f(-x) = f(x) ▪ Called an “even “ function ▪ Each term has a variable with an even exponent or is a constant Example y = 2x⁴ - x² + 2

2) Symmetric with the origin - ▪ (x,y) and (-x,-y) are points on the graph ▪ graph unchanged by rotation of 180° ▪ f(x) = -f(x) ▪ Called an “odd” function ▪ Each term has a variable with only odd exponents and can have no constants. Example y = 2x³ - x

Neither “odd” or “even” symmetry If it doesn’t fit all the “even” properties or all the “odd” properties then its NEITHER

Is it odd, even or neither? 1)f(x) = x¯² 2)f(x) = 3x³ + 2x² + 1 3)f(x) = x² + x 4)f(x) = x⁷ - x⁵ 5)f(x) = x³ - 1 6)f(x) = 1 - x⁴

Finding the intersection of 2 functions 1)If possible get y by itself on the left side of the equation. 2) Set the right sides equal to each other 3) Solve for x (usually involves factoring)

Try these: 1)x² - y = 3 and x – y = 1 2)x² + y = 7 and 2x – y = 1