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Pre-calculus Semester 1 Final
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Gravity
Key Concepts:
Terms in this set (55)
Set
A group of numbers.
Domain
The input set of a function.
Range
The output set of a function.
Function
Takes a number in one set and transforms it into exactly one number in another set.
Domain Function (equation)
{xER|0<x<1}
How many ways can you represent a function?
4
Graphically
Algebraically
Verbally
Numerically
Algebraically
Numerically
Graphically
X-coordinate
The input value
Y-coordinate
The output
Arithmetic Functions
f(x)+g(x)=(f+g)(x)
f(x)-g(x)=(f-g)(x)
f(x)
g(x)=(f
g)(x)
f(x)/g(x)=(f/g)(x)
Function Composition
A way to combine fractions not using addition, subtraction, multiplication, division
Parent Graphs and Transformations
y=x^2 (parabola)
y=x^3
y=|x| (absolute value)
y=square root of x
Inverse Function
A function that uses the range of another function as its domain and the Domain of the other function as its range is called an inverse.
Line
A function of 2 variable with no exponents
For lines we need 3 pieces of information
two points given
point and slope
slope and intercept
Mathematical Model
A way to describe some situation with math.
Linear Models
Some quantity is directly responsible for the other quantity.
R^2
A correlation coefficient
Graphing
Allows you to find the vertex easily.
Degree of a polynomial
A polynomial is said to be of degree "n" when n is the largest exponent
Solution
A number that makes an equation true.
Quadratic
A polynomial with degree 2
i^2
-1
Complex numbers
A number is complex if it includes both a real part and an imaginary part.
Fundemental Theorem of Algebra
A polynomial of degree n will have n roots in the field of complex numbers.
Des Cartes Rules of Signs
tells how many positive and negative real roots there are.
Rational Root Theorem
If a polynomial has a rational root it must be a divisor of the non variable term.
Even Functions
Symmetric on the y-axis
Odd Functions
Symmetric on the origin
Rational Function
A function created by the ratio of 2 polynomials
Vertical Asymptote
A vertical line that a function arbitrarily close to. The function will never cross a vertical asymptote.
Hole
A spot on a rational function that is undefined.
Horizontal Asymptote
A horizontal line that the function gets colser and closer to as x gets bigger and bigger or small and smaller.
Interval Notation
A way to represent an interval of numbers.
And
both inequalities are true.
Or
Only one or must be true.
Elimination
adding equations
Substitution
Substituting one variable into another equation.
Unique Solution
Need the same number of equations as you have variables.
Planes
Never intersect all together at all.
Consistent
The three intersect along 1 line or at one point.
f(x)=a^x
an exponential function
Exponential Growth
f(x)=a^x
Exponential Decay
f(x)=(1/a)^x
Euler's number
e=2.71828...
Amount of Money Investment Earns
T=Pe^rt
Centerpoint
Center
Radius
The distance to the outside of the circle to the center.
Standard From of a Circle
(x-k)^2+(y-h)^2=r^2
Standard Form
y+a(x-k)^2+h
Asymptote
A line that the function gets arbitraily close to
Logarithmic Functions
Always have a vertical asymptote.
Exponential Function
Always have a Horizontal asymptote
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