Functions and rates of change
Polynomial functions
Rational functions and inequalities
Exponential and logarithmic functions
Trigonometric radians,functions, identities and equations
100
What is a function
A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
100
what is a polynomial function?
a polynomial is an expression of finite length constructed from variables (also called indeterminates) and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents.
100
What is a rational function?
a rational function is any function which can be written as the ratio of two polynomial functions. Neither the coefficients of the polynomials nor the values taken by the function are necessarily rational numbers.
100
What is a logarithmic function?
The logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: 1000 = 10 × 10 × 10 = 103. More generally, if x = by, then y is the logarithm of x to base b, and is written y = logb(x), so log10(1000) = 3.
100
what is a trig function?
the trigonometric functions (also called circular functions) are functions of an angle. They are used to relate the angles of a triangle to the lengths of the sides of a triangle. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.
200
rate of change?
The change in the value of a quantity divided by the elapsed time. For a function, this is the change in the y-value divided by the change in the x-value for two distinct points on the graph. Note: This is the same thing as the slope of the secant line that passes through the two points.
200
what does polynomial mean?
it means many, binomial means two
200
How can you determine the vertical asymptote from the equation?
by finding the zero of the denominator
200
exponential?
A function whose value is a constant raised to the power of the argument, esp. the function where the constant is e.
200
what is a trig identity?
equation involves trig ratios and is true for all values of the variable for which the expressions on both sides are defined
300
What is the formula of a difference quotient?
f(a+h)-f(a) divided by h
300
How do you divide polynomials?
using synthetic or regular polynomial division
300
how are end behaviors of rational functions determined?
horizontal asymptotes or oblique asymptotes
300
what equation is the inverse of an exponential function be written?
y=logax
300
How can you solve a linear trig equation?
algebraically, using special triangles, calculater, sketch of the graph or the CAST rule
400
In what order are transformations performed?
stretches, compressions, reflections perform all translations
400
How do you factor a polynomial of degree three or greater?
use the factor theorem to determine one factor of the polynomial, and then divide to find other factors
400
How do you determine the avg or instantaneous rate of change of a rational function?
at points within the domain of the function using the same methods that are used for poly functions
400
if log involves base 10? how can a calculater be used to solve this
a calculater can be used to determine log10, to power of 25= log 25=1.39
400
To prove that an equation is not a identity you can use this counterexample?
LS doesnt equal RS
500
If you are given the graphs of or equations of two functions how can you create a new function?
by adding, subtracting or multiplying the two given functions
500
factor 27x3 - 64 ? think sum or difference of cubes
(3x)3 - (4)3 (3x-4)(9x2+12x+16)
500
when is it not possible to determine the avg or instantaneous rate of change of a rational function?
at a point where the graph has a hole or a v.a
500
how to simplify expressions that contain logs?
logs are written with the same base, you can simplify using laws of log that correspond to relevant exponent laws
500
What strategies can you use to solve a quadratic trig equation?
factor it, use Pythagorean identity or a graphing calculater
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