1. Chapter 3 Review
The nature of Graphs

2. Odd/ Even functions Odd function: f(-x) = -f(x)
Which means it has origin symmetry
-it can be flipped diagonally across the origin (y=x line)
*ex) y= x³
Even function: f(-x) = f(x)
It has Y axis symmetry
-can be flipped over y axis
*ex) y = x⁴

3. Families of Graphs  Constant function Y remains the same
Linear Equation
(Straight line)

4. Families of Functions continued 
Polynomial
(X to a power)
Square root function
(y= )
Y = x²

5. Families of Functions continued 
Absolute Value
(shape of a V)
* Greatest Integer function (step)
-y is the same for an entire integer
(ex from 1.01 to 1.99 y=1)

6. Families of Functions continued 
Rational Functions
(a.k.a. fractions,
and it has asymptotes)
Ex) y=
Y = ( - 1) +2

7. Trig Graphs 
Sine/ Cosecant
Sin/Csc

8. Trig Graphs Continued 
Cosine/ Secant
Cos/Sec

9. Trig Graphs Continued 
Tangent
Tan
Cotangent
Cot

10. How to move a graph
Reflections Y = - f(x) is over the X axis (How to remember: f(x) is the same as Y, so if the negative is outside, it does NOT affect the Y axis) Y = f(-x) is over the Y axis (How to remember: f(x) is the same as Y, so since the negative is inside, it DOES affect the Y axis)

11. How to move a graph Translations Y = f(x) +c is moving c units UP
(its adding height)
Y = f(x) –c is moving c units DOWN
(its subtracting height)
Y = f(x + c) is moving c units left
(if its inside the parenthesis, it will go in the opposite direction of the sign)
Y= f(x – c) is moving c units right

12. How to move a graph
Dilations To expand a graph horizontally (wider): Y = f(cx) and c is a fraction between 0 and 1 To compress a graph horizontally (skinnier): Y = f(cx) and c is greater than 1 To expand a graph Vertically (taller): Y = c·f(x) and c is greater than 1 To compress a graph Veritcally (shorter): Y = c·f(x) and c is a fraction between 0 and 1

13. Inverses To find an inverse:
Whether it’s an equation, graph, or a table, switch x and y
Then, solve for y if its an equation
Use the vertical line test on the inverse to figure out if the inverse is a function
Vertical line test is: if there is two different y values for one x (the vertical line hits the graph twice) then the inverse is NOT a fuction
Way to remember-
I:SSV
Inverses: switch, solve, vertical line test
I smell stinky vomit

14. Continuity/ Discontinuity
A graph is continuous if it has no breaks and there is a y value for every x value in the given interval
Infinite discontinuity: y keeps increasing or decreasing as you approach the x value in question (like a graph right before an asymptote)
Jump discontinuity: the graph stops at a certain y value on the x axis, and continues at a different y value on the same x axis (like the step graph)
Point discontinuity: The graph is missing a point (function does not exist at that point, but if the point were inserted the graph would be continuous)

15. End Behavior
End behavior = what the y values of the graph do as X goes to ± infinity Ex) *as x approaches infinity, y increases *as x approaches negative infinity, y also increases
Y = x²

16. Critical Points
Maximum (when the function is increasing to the left of x=c and decreasing to the right of x=c, then the maximum is x=c)
Minimum (when the function is decreasing to the left of x=c and increasing to the right of x=c, then the minimum is x=c)
Point of inflection (graph changes curvature/concavity, a.k.a. curving up or down)
Absolute Max (the point at which the highest value of the function occurs. x=m)
Absolute Min (the point at which the lowest value of the function occurs. x=m)
Relative Max (not the highest point in the function, but the highest point on some interval of the domain x=m )
Relative Min (not the lowest point in the function, but the lowest point on some interval of the domain x=m)

17. Rational functions F(x) = Where G(x) cannot equal zero (undefined)
Asymptote: Horizontal = Y = = = Y
Vertical = use G(x) = 0 to get the
X value of the vertical asymptote

18. Variation Direct: Y = k · x^n a.k.a. Y= kx Inverse: Y = a.k.a Y=
Joint:
Y = k · x^n · z^n

19. Bibliography