Math (4-5) Test Review
Quadratic Function: Domain and Range are both
(-infinity,infinity)
(X^3 +- a^3)
(x+-a)(x^2 -+ ax ++ a^2) x^3-8 = (x-2)(x^2 + 2x + 4)
When you do not include x or y on a graph, the interval notation looks like
(x, y)
When given a graph and asked Solve f(x)>6...
(x,6) Not including x to infinity
The x-coordinate of the vertex of f (x) = ax squared + bx + c, a≠0, is _______.
-b/2a
How many solutions does x have
1(+ or -)
What is a polynomial?
An equation with at least x^3 and has no x's in the denominator
Domain for rational function : When it's in the denominator
Do NOT include in interval, use parenthesis y=(x+1)/x - Domain - (-infinity , 0)U(0, infinity)
Linear Graphing step 2: f(x) = mx +b
Find y-intercept
When asked to graph and find the point that represents the solution to the equation f(x) = g(x)...
Graph the solution and the point that intersects both is the solution
If the slope m of the graph of a linear function is _______, the function is increasing over its domain.
Increasing
In a quadratic function, if there is a negative in front of the x...
It opens down
Solve f(x)=g(x)
Set f(x) equal to g(x) 3x+4 = 4x+5
If b2−4ac > 0, which of the following conclusions can be made about the graph of f(x) = ax2+bx+c, a≠0?
The graph has two distinct x-intercepts.
When it's greater than or equal to/ less than or equal to
Use brackets
axis of symmetry
x= x value ofvertex
A car has 12,500 miles on its odometer. Say the car is driven an average of 40 miles per day. Choose the model that expresses the number of miles N that will be on its odometer after x days.
N(x)=40x+12,500
Real Zero's of a Polynomial
Real Zero's of a Polynomial = x-intercept. No x-intercept means no real zeros.
(f(x) = 4x +3) When f(x) = 0...
Set it equal to 0 (0=4x + 3)
The graph of f(x)=4x2+5x−7 opens up. true or false
True Parabola will open up if a is more than 0
Use parenthesis when
You DO NOT include a number
Use brackets when
You DO include a number
Minimum value
a is bigger than 0
How many solutions does x^2 have
2 (+ and -)
complete the square step 2 a(x^2 + bx/a) + c
Factor x, get x by itself a(x+b/2a)^2 + c - (b/2a)^2
Rational functions when n = d
HA at quotient of leading coefficient
Domain for rational function : When it's in a square root
INCLUDE x, use brackets y=squareroot(x-5) - Domain - [5, infinity)
When analyzing a rational graph,
Plug in points
The y-coordinate of the vertex of f(x)=−x2+4x+3 is f(2). True or false
The statement is true because the x-coordinate of the vertex is 2
If the discriminant b2 − 4ac=0, the graph of f(x)=ax2+bx+c, a≠0, will touch the x-axis at its vertex. True or False
True
Where is g(x) greater than f(x) on a graph?
Use intersection y values
When is a function increasing?
when the slope is positive y=x y=x^2 from 0 - infinity
When Solve the inequality f(x)>g(x).
will be in interval notation
Equation of a line When asked for the axis of symmetry
x = the x value of the vertex
When solving for an inequality, when do you use union
After you plug in a number inbetween solution and it makes the function not true
The vertical line passing through the vertex of a parabola is called the ______.
Axis of Symmetry
Domain for rational function : When there's a square root in the denominator
Do NOT include x in interval, use parenthesis y = x/squareroot(x+2) - Domain - (-2, infinity)
The average rate of change of f(x) =3x +9 is 9. True or false
False
Linear Graphing step 1: f(x) = mx +b
Find slope
rational function graph when numerator is smaller than denominator
HA is at y= 0
What is the only type of function that has a constant average rate of change?
Linear Function
Direction of inequality changes when
Multiplied by a negative
When writing domain, what should you look for?
No 0's in the denominator and no negative numbers in square roots
Infinity will always be in a ?
Not including, parenthesis
The graph of a quadratic function is called a(n) _______.
Parabola
Quadratic Formula from vertex and the y intercept step 2
Plug in point to x and y into y= a(x-h)^2 + k Solve for a Plug a back into y= a(x-h)^2 + k
Quadratic Formula from vertex and the y intercept step 1
Plug in vertex to y= a(x-h)^2 + k h is x of vertex k is y of vertex
For the graph of the linear function f left parenthesis x right parenthesis equals mx plus bf(x)=mx+b, m is the _______ and b is _______.
Slope, y-int
Solve f(x)≤g(x)
Solve for x: 4x+3 ≤ 4x + 5
For what values is this true: f(x)>0 (f(x) = 4x +3)
Solve for x: 4x+3 >0
When a is not 1 in a quadratic formula
Split a into x coefficients
complete the square step 1 Given (ax^2 + bx + c)
Take a out and out it in the front a(x^2 + bx/a) + c
n (numerator) is one more than d (denominator)
There's an oblique asymptote, long division
The slope of a nonvertical line is the average rate of change of the linear function. True or False
True
When it's greater than or less than
Use parenthesis
Asymptote solution sets
Use parenthesis on asymptote
When determining solution to a quadratic formula with a graph
Use x values
muliplicity
What power the equation is (x-3)^2 has a multiplicity of 2
What is a hole?
What the domain doesn't include and whatever cancels out
Quadratic Formula
[-b ± √(b² - 4ac)] / (2a)
When including x on a graph, but not y, the interval notation looks like
[x,y)
When including x and y on a graph, the interval notation will look like
[x,y]
When forming a polynomial, what do you include/ What are you solving for (How do you solve it)
a (A is a leading coefficient) DONT EXPAND Plug in given x and y
If the graph of f(x)= ax2+bx+c, a≠0, has a maximum value at its vertex, which of the following conditions must be true?
a is less than 0
Maximum Value
a is smaller than 0
vertical line test
a visual way to determine if a curve is a graph of a function or not.
Determine the turning points of a polynomial function
highest power - 1
to find y intercept
plug in 0 for x
Quadratic equation, to find vertex, -b/2a is x, then..
plug your answer in the original equation
To find an x intercept
set = 0
Finding Average Rate of Change for linear functions
the slope
When finding an x-intercept in a polynomial function
use real zeros and set equal to 0
