Study Flashcards
What do real number include?
Include Irrational, rational, and integer numbers.
Include Irrational, rational, and integer numbers.
Real numbers
What does the € symbol mean?
“In”
Symbol that means “in”
€
The four ways to represent a function?
Graphically, algebraically, numerically using tables, verbally.
Graphically, algebraically, numerically using tables, verbally.
The four ways to represent a function
What makes graph not a function?
Does not pass vertical line test and has has two values of y for every x.
Does not pass vertical line test and has has two values of y for every x.
Not a function.
Draw graph of hot water faucet.
S
How is this factored?:
2x^2-5x-12
Multiply the first and last constants and see what adds to the second number and multiplies to the last.
Multiply the first and last constants and see what adds to the second number and multiplies to the last.
Dealing with unfactorable functions.
How do you test if two functions (f(x) and g(x)) are inverses of each other?
Plug g(x) into f(x) and f(x) into g(x) and if you get x on both functions, they are inverses.
How is the function f(x)=|x| written in piecewise form?
{ -x if x< 0
{ x if x>= 0
{ -x if x< 0
{ x if x>= 0
Piecewise version of the function f(x)=|x|
How can you test if a function is even?
If its graph is symmetric across the y-axis and f(x)=f(-x)
If its graph is symmetric across the y-axis and f(x)=f(-x)
Testing if a function is even.
Increasing function definition.
x1 < x2 and f(x1) < f(x2)
x1 < x2 and f(x1) < f(x2)
Increasing function definition
In an even function on the graph, is the function increasing or decreasing?
Neither (points upward both sides)
When is a function neither increasing nor decreasing on a graph?
When it is even (points upward both sides)
3 examples of real world mathematical models of functions.
Population size, demand of a product, falling object
Population size, demand of a product, falling object
Examples of real world mathematical models of functions.
Slope intercept form
y=mx+b
y=mx+b
Slope intercept form
Point Point form
m=y2-y1/x2-x1
m=y2-y1/x2-x1
Point Point form
How is a polynomial function defined?
P(x)=a(n)x^n + a(n-1)x^n-1 + … a(1)x(1) + a(0)
P(x)=a(n)x^n + a(n-1)x^n-1 + … a(1)x(1) + a(0)
Polynomial function definition
What is the domain of a polynomial?
All reals
Have domain of all reals
Polynomials
How many roots does the graph of a function NOT touching the x-axis have?
None
What kind of graph of a function has no roots?
A function not touching the x-axis
How can you tell how many roots a function has with this?:
b^2 -4ac
< 0, no real roots
> 0, 2 real roots
= 0, 1 real root
< 0, no real roots
> 0, 2 real roots
= 0, 1 real root
Using b^2 -4ac to find roots
Power function
f(x)=x^a where “a” is a real number
f(x)=x^a where “a” is a real number
Power function
What makes a function not a polynomial?
Power is not an integer
When the power of a function is not an integer, it is not a
Polynomial
How do you graph ^3√x or any other odd denominator power?
Similar to x^3 but the graph gets flatter along the y-axis
Similar to x^3 but the graph gets flatter along the y-axis
Graphs with odd roots as powers
Graph f(x)=x^-1 OR 1/x
A
What is a hyperbola?
Function with x and y-axis’ as its asymtotes
Function with x and y-axis’ as its asymtotes
Hyperbola
How is a rational number defined?
P/q, where both P and q are integers
P/q, where both P and q are integers
Rational number
What does the “pipe” “|” mean in a domain?
“Such that”
Means “such that”
“Pipe” “|” in domains
How makes a rational function?
Square roots or division
Square roots and division make what kind of function?
Rational
How is a sin graph plotted?
With 0 at 0 and period every π
With 0 at 0 and period every π
Sin graph
How is the cos graph plotted?
0 at 1 and period every π/2
0 at 1 and period every π/2
Cos graph
What is odd and what is even?:
sin and cos
Sin is odd, cos is even
What is the domain of sinx/cosx and why?
{x€R|x≠π/2 + nπ} because every π/2, sin is 0. Adding π to π/2 gives another multiple of π/2.
What are three features of polynomial graphs?
No breaks, holes, or corners
No breaks, holes, or corners
Polynomial graphs
What is a characteristic of log graphs?
They always have (1,0) as a point
They always have (1,0) as a point
Log graphs
Exponential function definition
b^x ehere b>0
b^x ehere b>0
Exponential function
Characteristic of exponential function graphs
Always hit the point (0,1)
Always hit the point (0,1)
Exponential functions
What happens to a log graph as the base gets bigger?
It gets lower and closer to y-axis
Gets lower and closer to y-axis as base b gets bigger
Log graphs
What is vertex form?
y=a(x-h)^2 +k where (h,k) is the vertex
