Passport to advanced math

Question 1

Functions. F(0) =3 what is x and y

Answer 1

x=0, y=3

Question 2

Tables, they may give you tables for functions and you need to know how to deal with it.
Ex. f(p) =3 what is p.

Answer 2

To find p, you simply go the y axis of 3 and find the x value

Question 3

Graph translation rules. F(x+1) and . F(x)+1 -f(x) f(-x)

Answer 3

F(x+1) = graph moves left 1. F(x)+1 = graph moves up one
-f(x) = y values negated (means opposite -3=3): reflection on the x-axis
f(-x) = x-values negated: reflection on the y-axis
Tip: when you have a reflection no the y-axis, the y-intercept remains the same. And the slope stays the same as well. The intercepts that dont stay the sa,e are the ones negated

You can graph this by finding the negation of the numbers and plotting them

Question 4

Negative numbers will turn positive when, but stay negative when

Answer 4

Negative numbers will turn positive when raised to even powers, but stay negative when raised to odd powers

Question 5

Exponentuons function, growth and decay. Expoenntnons functions grow when and decay when Ex. y=(0.75) squared x.

Answer 5

Exponentuons function, growth and decay. Expoenntnons functions grow when the base is grater than 1, and gets smaller when the base is between 0 and 1.
Ex. y=(0.75) squared x.
Since 0.75<1, y decreases as x increases

Question 6

Bionomal squares: Difference of two squares:

Answer 6

Bionimla: (x+y) squared = x2+2xy+y2
(x-y) squared = x2-2xy+y2
Difference of two squares:
(x+y) (x-y) = x2-y2

Question 7

Parabolas are, and what is the stanard form and what do the coeffectens tell you./

Answer 7

Satnard form of a parabola. Y= ax squared +bx +c
Coeefeicents tell you that the constant a tells you wheter the parabola opens up or down. If a is negative then it has a forwny face.

The cosant c is the parabolas y-intercept, if there is no c, y-intercept = 0
The vertex of the parabola is -b/2a to find the x coordinate

Question 8

Factored form of a parabola.

Answer 8

Y = a(x-m) (x-n)
The constant m and n tell you the parabola x-intercept
A tell you whether the parabola goes up or down.
If you neded to convert ot standard or vertex form, your first step is to foil

Question 9

If presented parabola questions and not enough information to quickly derive an equation, think symmetry
Each point on the parabola to the left of the line will have a

Answer 9

a point mirroning it. Ex, if parabola point x= -3 and x = 3. Then there will be a point x=0 since its the vertex and middle of them

Question 10

Polynomials. What are zeros and how to calculate

Answer 10

Zeros, are the time when the graph hits the x-values
To calculate zeros, you need to know if that x=3, then x x-3 is a factor of the polynamials
Long division, finding reminders and when asked to divide you do:
Polynomial, means multiple terms