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Functions and Graphs Concept Map (How to write Linear Equations (Two…
Functions and Graphs Concept Map
Term
The word for a number or function in an expression
Expression
An expression is similar to a equation but does not contain and equal sign
Equation
A series of terms or values that equate to a solution and contains and equal sign
Exponent
The power a number or expression is being raised to
Function
Expression with one or more variables and has a single output
Features of a Function
Intervals of increasing value
This means that slope is increasing and both the X and Y values are increasing
Intervals of decreasing value
This means that the slope is decreasing and both the X and Y values are decreasing
Zeros
zero in a function as an input will result in an output of zero
Maximum
The highest number
Range
difference between highest and lowest values
Minimum
The lowest number
Domain
set of all possible x-values that work and will give a real y-value
Asymptotes
a line that approaches the curve but does not meet the line
Quotient Rule for Exponents
When you are dividing two numbers with exponents, the numbers need to be the same and then you can subtract the exponents
Negative Exponent Rule
A negative exponents shows how many time to divide the number by itself.
Power Rule for Exponents
When multiplying two exponents by the same base, you can add them together.
Product Rule for Exponents
When you need to multiply two numbers with exponents, the numbers need to be the same and just add the exponents
Fractional Exponents
The use of fractional numbers as exponents
Zero exponent Rule
Any number or expression with a exponent of 0 is equal to 1
Slope
Graphical Form
In graphical form slope is represented by a linear line that has an intercept on the X and Y axis
Real Life Examples
Carlos bought a car for $72,000 and every year it decreases 6,000 dollars.
A forensic investigator finds the post mortem interval because she knows body temperature decreases 1.4 degrees per hour from its original 98.6 degree temperature.
Numerical Form
In numerical form, slope contains a Y set equal to the slope multiplied by the variable and then added to the intercept
How to write Linear Equations
Two points on a line
Slope and a point
Slope and an Intercept
Graph of line
Slope intercept form
Point and the equation of a parallel line
Point and the equation of a perpendicular line
Evaluating Functions
Function Notation - an effective and efficient way to evaluate mathematical functions
Value of using function notation is that it can show a point and makes it clear what function you're referring to.
Piecewise Function
A piecewise function is a function that is defined by multiple sub functions make up the main function.
Parent Functions
Here they are
Quadratic
The Domain is
and the Range is
The minimum is (0,4)
Radical
The Domain is
and the Range is
Linear
y = x
The Domain and Range is
Rational
The Domain is
and the Range is
There is a vertical asymptote at x=8
