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Functions and Graphs Concept Map (Slope (How to Write Linear Equations…
Functions and Graphs Concept Map
Quotient Rule
Negative Exponent
Negative exponents: Flip and become positive
Product Rule
all of the bases have to be the same
Fractional Rule
Zero Rule
Power Rule for Exponents
Vocab
Term: a term is a single number, constant, or a variable that can be multiplied by a variable to get an answer (x=4)
Expression: terms that can be added, multiplied, divided or subtracted from each other (4x/3 + 2x/1)
Equation: this shows that two expressions can be equal to each other (4x-1=3y)
Exponent: a number that shows how many times you can multiply another number (8^)
Function: each input has a single output
Slope
This is how a line can be measured as a way to show the rate of change.
Rate of Carbon Dioxide atmospheric concentration in parts per million.
Slope and a Point: Given m=2 and point (-1,-6)
How to Write Linear Equations
y=mx+b In this case the m value is the slope, and the b is the y-intercept.
if m equals 1/2 and b equals 6
Two Points on a Line: Given points (1,2) (3,4)
Graph of a Line: Given the graph shown, the line crosses at 7, and the slope would be 2/3 because it rises 2 and runs 3.
Graph:
https://drive.google.com/open?id=188JA8dIiAXn75G2EX0uHnBMl_KJUL7hy
Point and the Equation of a Parallel Line: Given the through point (-2,1) and parallel to y=-1/2x
Point and the Equation of a Perpendicular Line: Given the through point (-2,3), and perp to y=-3/4x
flip the slope
This is the depreciation rate of new cars after you purchase them.
Function Notation
Function Notation is the labeling of functions to avoid confusion while having many on one graph.
For Example: f(x) Means Function of x
f(g) stands for function of g so that you can avoid confusion in the use of variables so that y doesn't equal multiple values in a graph.
Other examples:
f(Carbon) f(Noodles)
In this example at x+1 there are three different y values for x but for f(green) y=1 f(red) y=7.9 f(blue)=7
The x value could also be replaced with an expression. so f(x)=√x-2. x could be replaced with (x-6).
Domain:All .of the possible x values in a function
Range: All of the Possible y values in a function
Zeros: Where the intersects an axis
Intervals of Increasing values:
Intervals of Decreasing values:
Maximums: The highest a function goes
Minimums: The lowest a function goes
Asymptots: A line that a function will get infinitely close to but never cross.
Parent Functions.
x=y
This is a simple linear equation with a positive slope of 1.
\( y=x^2\) This is the simple positive parabola and a quadratic equation.
\( y=(x-1)^2 -2\)
This shows a two unit shift right and a single unit shift down
y=|x| This is the absolute value parent function.
y=√x This is the radical parent function
y= log(x) This is the logarithmic parent function.
:
Piecewise Function
These are functions that are essentially broken up into things called "sub-functions" . Where all of the functions are broken up so that there are multiple on a single graph with none of the same values.
example graph
https://drive.google.com/open?id=1jVZbCfey1K47HMsaoG941mOGvOeVrUY3
