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Math Concept Map (critical features of a function (range (the set of y…
Math Concept Map
critical features of a function
range
the set of y-values of a function or relation.
domain
the set of values of the independent variables for which a function or relation is defined.
zeroes
where a function equals the value zero.
intervals of increasing/decreasing value
intervals of increase and decrease are the domain of a function where its value is getting larger or smaller.
maximums
the largest value of a function.
minimums
the smallest value of a function.
asymptotes
a value that you get closer and closer to, but never quite reach. in other words, an asymptote is a horizontal, vertical, or slanted line that a graph approaches but never touches.
Linear Equations With Different Knowns
Point and the Equation of a Perpendicular Line
When solving a perpendicular slope equation, Flip the slope and change the sign.
Two Points on a Line
If you know two points, you have to subtract y1 from y2 and subtract x1 from x2.
Graph of a Line
When finding the slope of an equation with just a line on a graph, find two points and subtract y1 from y2 and subtract x1 from x2.
Slope and a Point
y = point we don't know, y1 = point we do know, m = slope, x = point we don't know, x1 = point we do know
Point and the Equation of a Parallel Line
When solving a parallel slope equation, don't do anything to change the slope because the slope is the same if it's parallel.
Slope and an Intercept
m = slope, x = starting point, b = intercept
Six Parent Functions
Linear: The equation of the linear parent function is y = x. The slope, or rate of change, is constant
Quadratic: Quadratic functions form parabolas on a graph. It's a U shape and its simplest form is y = x^2
Absolute: An absolute value function is a function that contains an algebraic expression within absolute value symbols. It forms a V-Shape when graphed.
Rational: A rational function is f ( x ) = 1 x and the graph is a hyperbola. In a rational function, an excluded value is any -value that makes the function value undefined.
Logarithmic: Logarithmic functions are the inverses of exponential functions. The inverse of the exponential function y = a^x is x = a^y. The logarithmic function is
y = log a^x.
Radical: A radical function contains a radical expression with the independent variable (usually x) in the radicand.
Functions
Function Notation
is how a function is written, that gives precise information without a lengthy explanation.
Value
is when given multiple equations it's easier to keep track of the y values, also when looking for a point in data, the f(x) function gives more information than y=x.
Examples
Numbers
Expressions
piecewise functions
is a function defined by at least two equations, representing the different pieces, each of the pieces apply to one of the domains.
https://docs.google.com/document/d/1RSTZkv6qCNK9kGAzDcebgItK-8f6aGorJLkbTcT9CP4/edit
Power Rule for Exponents:
When raising a power to another new power, multiple the exponents.
equation
an equation is a statement that two things are equal, consisting of two expressions, one on each side of an '=' sign.
3 x 4 = 12
7x – 5 = 4x / 2
term
a term is a single number or variable, or numbers and variables multiplied together.
4x
–
7
=
5
the terms are separated by the operators, making 4x, 7, and 5 the terms of this equation.
exponent
the exponent of a number defines how many times to use that number in a multiplication.
because 8 is raised to the third power, 8 will be multiplied against itself 3 times. 8 x 8 x 8.
expression
an expression is a phrase that can contain numbers (1, 2, 3), variables (x, y), and operators (+, –, /, x).
1 + 2
2 x 3
function
a function is a relationship where each input has a single output.
Zero Exponent Rule for Exponents
: Any number raised to 0 is equal to 1.
Quotient Rule for Exponents:
To divide two exponents with the same base, you keep the base and subtract the powers.
Product Rule for Exponents
: When multiplying two powers that have the same base , add the exponents.
Negative Exponent Rule
: Negative exponents switch positions from numerator or denominator and become positive.
Fractional Exponents Rule:
Slope
: Slope is a rate at which something inclines or declines.
Graphical Form:
Numeric Form:
Real Life Examples of Slope:
When I'm shopping, an apple cost 2$ but after I buy 5 they cost 1$ for any more. The first 5 cost 2$ and any more cost 1$. I bought 8 Apples and spent 13$. The cost is then falling and can be shown in slope form.
The slope of a rollercoaster with a height of 139 meters and a width of 60 meters has a slope of 139 over 60.
https://docs.google.com/document/d/1DMjSPkHZg1KbbqV9szT-O2HscUKHl2ZyMVnVxfPCC-w/edit
https://docs.google.com/document/d/1DMjSPkHZg1KbbqV9szT-O2HscUKHl2ZyMVnVxfPCC-w/edit
