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When in the equation, this is what the greater than or less than represent. they mean when they are graphed.
- These are functions that are represented by a combination of equations, each corresponding to a part of the domain.
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
Both rational examples can be seen.
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 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:
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.
This rule states that when two numbers are multiplied with exponents, if they have the same base, the exponents can just be added.
Example:
This rule sates that to raise a power to another power one need's to multiply the exponents together.
Example:
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:
(X1, Y1) is one point (X2, Y2) is another point
It is used to find the slope.
This rule states that any number raised to the "0" power is always 1.
Example:
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:
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
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 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.
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.