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Calculus Concept Map

By: Lee Kennedy & Ryan Reagan

THE END

Piecewise Continued

When in the equation, this is what the greater than or less than represent. they mean when they are graphed.

Determining Domain of Piecewise Functions

How to Graph a Piecewise Function

Piecewise Function

- These are functions that are represented by a combination of equations, each corresponding to a part of the domain.

Parent Functions

Parent Functions Continued

On the quadratic graph the max and min can be seen through the Domain and the Range. The ma is the highest point and the min is the lowest point.

Parent Function Examples

Function Notation Examples

Both rational examples can be seen.

Function Vocabulary

Parent Function Examples

Three Examples of These Rules...

Domain - The set of all possible input values (commonly the "x" variable), which produce a valid output from a particular function.

Range - The range is the set of all possible output values (commonly the variable y, or sometimes expressed as f(x)), which result from using a particular function.

Zeroes - Where a function equals the value zero (0). It is also called "root".

Intervals Increase - When the y-value increases so do the intervals.

Intervals Decrease - They decrease when the y-value gets smaller.

Maximums - These are the highest points of the graph that are displayed.

Minimums - These are the lowest points of the graph that are displayed.

Negative Exponent Rule

Negative exponents in a numerator are moved to the denominator to become positive and negative exponents in a denominator are moved to the numerator to become positive.

Example:

Linear Equation Given Graph of a Line

Choose two points on the line to determine the slope... (rise over run). Next, take the slope and one of the two points found and plug them into point slope equation.

Product Rule of Exponents

Parent Function Examples

This rule states that when two numbers are multiplied with exponents, if they have the same base, the exponents can just be added.

Example:

Power Rule for Exponents

This rule sates that to raise a power to another power one need's to multiply the exponents together.

Example:

Slope Definition

Linear Equation Given Slope & a Point

If we have a point, ( x1 , y1 ) , and a slope, m, here's the formula we

use to find the equation of a line

Graphical... Slope is the steepness of the line, aka, "rise over run"

Example:

Numerical... The change in Y over the change in X creates the slope. "Rise over Run" and steepness of the line.

Example:

Linear Equation Given Two Points on a Line

(X1, Y1) is one point (X2, Y2) is another point

It is used to find the slope.

Zero Exponent Rule

This rule states that any number raised to the "0" power is always 1.

Example:

Quotient Rule for Exponents

Two Unique Examples of Slope as a Rate of Change

This rule states that the exponents are subtracted from one another if the bases are being divided. The numerator is being subtracted from the denominator.

Example:

Linear Equation Given Point & Equation of a Parallel Line

The slope of the line would match the original equations slope exactly. The intercept would be the only part of the equation that is different. Once this is find plug into y-y1=m(x-x1) equation.

Critical Terms

1) Slope can help determine the amount of goals scored per game.

- Henry T has 6 goals in 3 games. If he keeps scoring at the same rate how many goals will he have after 10 games?

He will have 20 goals after 10 games

The slope would be 2 goals every game

2) Slope can also determine how many slabs of fudge one has after a certain amount of time if some are eaten.

- Henry T has 20 slabs of fudge, after 1 week he only has 13. How many will he have after 2 weeks?

He will have 8 left after 2 weeks

He goes through 1 slab every day

Definition... Function Notation

Function notation is the algebraic method of writing functions of other variables. They are used as the example f(x) and is a way to determine what the value of X is when the Y is given.

Term: a single number or variable, or numbers and variables multiplied together.

Example: 3x, 3

Expression: Contains ordinary numbers, variables and operators.

Example: X and Y variables... Operators = * & /

Equation: a statement that the values of two mathematical expressions are equal.

Example: Y = 2x + 123

Exponent: a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression.

Example: 5^2 means 5 is raised to the second power.

Function: Is a relationship that involves more than one variable.

Example: f(x) = 3 +2x, x = 4

Fractional Exponents Rule

Linear Equations When Given Slope & a Intercept

Fractional exponents are changed to a square root. With the denominator as the root and the numerator as an exponent.

Example:

One would use the equation Y = Mx + B... Where (M) is the slope and (B) is the intercept.

Linear Equation Given Equation of a Perpendicular Line

Function Notation to Define a Equation

The function is defined by function notation. f(x) replaced by x in the equation and that is what is known. The Y is given in the form of F(x) and one solves for the X.

If the line is perpendicular, the slope would be the opposite reciprocal of the original equation's slope.

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