Nomials
What is a binomial
An algebraic expression of the sum or the difference of two terms
What are domain and range
domain is: The set of all inputs of a function (the x-values or independent variables).
Range is: The set of output values of a function (the y-values or dependent variables).
A function is given by the set of ordered pairs ?(2, 5) (4, 9) (6,13) (8,17). Write its domain and range in roster form.
Domain (2,4,6,8)
Range (5,9,13,17)
What is Proportional or Direct Relationship
Two variables, x and y have a direct (proportional) relationship if for every ordered pair (x, y) we have:
y/x = k or y = k*x
Stated simply, y will always be a constant multiple of x. The value of k is known as the constant of variation.
What is Point-Slope form of a line
y - y1 = m (x - x1); where m is the slope (average rate of change) and (x1, y1) is a point on the line
what is Cubic polynomial
A polynomial with its highest exponent of the variable as 3.
What is domain restriction
A limitation on the domain of a function, usually to represent only values that are realistic in a given context.
Examples include: Not dividing by 0 (or having it in the denominator) and not having a negative underneath a square root.
The function 2 h(x)=x2+5 maps the domain given by the set (-2, -1, 0,1, 2). Which of the following sets represents the range of h(x) ?
(5,6,9)
What is a constant variation and direct variation
Constant: A constant ratio in a direct variation. Represents the number k in equations of the form y=kx.
Direct: The relationship between two variable quantities that have a constant ratio.
What is parallel
Two lines that NEVER intersect
What is a trinomial and an example
An algebraic expression of the sum or the difference of three terms
What is a One-to-One Function
A function for which every y-value of the function corresponds to exactly one x-value.
In which of the following formulas is the variable y a one-to-one function of the variable x? (Hint – try generating some values either in your head or using TABLES on your calculator.)
1. y=x2 2. y=lxl
3. y=2x 4. y=5
3. y=2x
What is average rate of change
How steep a line is between two points on a graph. (another name for this is slope)
what is Reciprocal and an example
When the denominator and numerator are flipped
Find the product: (x-2)(x+4)(x-7)
x2-3x-28
What is a Horizontal Line Test and draw one on white board
If any of these passes through the graph of a function at most one time, then that function is one-to-one. This test works because it represents constant y-values; hence, if it intersects a graph more than once, an output has been repeated.
Find the inverse function
f(x)=3+1/5x
f-1(x)=5x-15
If x and y vary directly and y is 24 when x is 4 find y when x is 3
y=18
what is Perpendicular and draw an example on white board
Two lines that intersect to form right angles
solve for a polynomial: (2x-3)(4x2+5x-7)
8x3-2x2-29x+21
What is a Vertical Line Test and draw an example on the white board
A test used to determine whether a relation is a function by checking if a this line touches 2 or more points on the graph of a relation.
Evaluate the composition if f(x)=2x-1 and g(X)=3x+5 what is the value of (fog)(x)
6x+9
If x and y are in direct proportion and y is 12 when x is 6, find y when x is 5
y=10
Slope of perpendicular lines
Negative reciprocal of given slope