Section 1
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Cards (124)
Section 1
(50 cards)
range
set of all the possible y-values. OUTPUTS
other names for "y"
range, dependent variable, output
Integer
A whole number, both positive and negative numbers, including zero. ... ,-3, -2, -1, 0, 1, 2, 3, ......
Linear Function Parent Graph
independent variable
the INPUT or CAUSE in a situation or problem. It's the variable YOU CAN control. It's the X variable.
other names for "x"
domain, independent variable, input
Table
A way to represent ordered pairs.
what is the linear parent function?
y = x f(x) = x
changing the "b" in the slope-intercept form of the equation of a line changes what?
moves the line up or down the y-axis.
how is slope important for linear equations and lines?
linear equations and lines have CONSTANT slopes. The slope is the SAME all the way up and down the line.
Absolute Value Parent Function
words for ">"
is more than, is greater than, is larger than, shade above, shade to the right
What is a quadratic equation or function?
an equation of function that has "x-squared" as its highest order exponent.
dependent variable
the OUTPUT or RESULT in a situation or problem. It's the variable YOU CANNOT control. It's the Y variable. In a equation, its the variable BY ITSELF on one side of the = sign.
How do you DIVIDE exponents of like variables?
SUBTRACT them
How do you MULTIPLE exponents of like variables?
ADD them
Natural numbers
Counting numbers: 1, 2, 3, ......
How do the slopes of parallel lines compare?
They are the same
discreet function (scatter plot)
data appears as individual points on a graph. Whatever is being graphed cannot be broken down in to smaller pieces.
graph of exponential decay function
Whole numbers
Start with 0, 1, 2, ......
domain
set of all of the possible x-values. INPUTS
ordered pair
the x and y coordinates of a point on the coordinate plane (x,y)
words for "<"
is less than, is smaller than, shade below, shade to the left
in y = mx + b, "m" stands for?
slope
what slope does a VERTICAL line have?
undefined slope
How do you combine like terms?
Add their coefficients.
changing the "m" in the slope-intercept form of the equation of a line changes what?
the steepness of the line
what is the y-intercept?
the point where the graph crosses the y-axis. It has the coordinates (0, y)
relation
set of ordered pairs
function
special relation where each x-value is paired with ONLY ONE y-value. (x-values DO NOT repeat, it passes the vertical line test)
what slope does a HORIZONTAL line have?
slope = 0
Graph a parabola using a table
How do the slopes of perdendicular lines compare?
They are opposite and fraction is flipped. Example: lines with the slopes -2 and 1/2 are perpendicular.
graph of a quadratic function
in y = mx + b, "b" stands for?
the y-intercept
continuous function
data appears as a smooth curve on a graph.
Quadratic Parent Function
vertical line test
a relation is a function and passes the vertical line test if when a vertical line is drawn through the graph, it touches the graph only ONE time.
graph of exponential growth function
Where are the solutions of a quadratic function?
at the x-intercepts. They are also known as zeros and roots.
variable
NOT A NUMBER. A letter or symbol that stands for a number.
What is the "rate of change" on a graph?
Slope
what is the x-intercept?
the point where the graph crosses the x-axis. It has the coordinates (x, 0)
what is a linear inequality?
It is an equation with a <, >, < or =, > or = in the place of the =.
Mapping
Bubbles that represent the x-values and the y-values.
define slope
the steepness of a line, vertical change/horizontal change, (y-y)/(x-x), rise over run
coordinate plane
a plane formed by 2 perpendicular lines called axes (the x-axis goes sided to side, the y-axis goes up and down).
What are "like terms"?
mathmatical terms that have the SAME variables raised to the SAME exponents.
graph of a linear function
Section 2
(50 cards)
If y=f(x) and y=g(x), then.....
f(x) = g(x) meaning you can set the two equations equal to each other in order to solve for the variable. Then to find y you plug the variable back into one of the original equations and solve.
Step-Function Graph
A function that is not continuous. It has levels which represent the y-value for a set of x-values.
Interpret parts of an expression
Examples such as: C= 250 + 35m, Where C is the cost for renting a car. They pay $250 plus $35 for every extra mile they drive. You have to interpret what the numbers and variables mean in the form of a word problem.
Factoring with 3 terms
ax^2 + bx + c = 0, where a=1 (x )(x )=0 Find the two numbers that multiply to get you c, AND they add/sub to get you b. If asked to SOLVE by factoring, then set each factor equal to zero and solve.
How to tell when a function is increasing or decreasing?
Always read a graph from left to right, just like the words on a page. If it goes up, it is increasing. If it goes down, it is decreasing.
Which quantity increases fastest?
exponential functions > quadratic functions > linear functions
Distinguish between situations that can be modeled with linear functions and with exponential functions.
A linear function would be best for situation in which something is increasing at a constant rate. An exponential function is best for situations in which the rate increase over time. EX. The growth of bacteria cells in a petri dish would be exponential growth.
Arithmetic Sequence
A pattern in which you add a number each time.
The Square Root Property to solve Quadratics
To get rid of the exponent 2, you can take the square root of both sides. Remember the plus or minus symbol, which can give you two answers.
How do you multiply FRACTIONS?
Cancel or reduce if possible, then multiply straight across. Some people like to multiply straight across and then reduce. Either way, if you can reduce, you MUST REDUCE.
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal description.
For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
Maximum or Minimum
Maximum is at the highest point of a parabola. Minimum is the lowest point.
When do you flip an inequality symbol?
Anytime you multiply or divide by a negative number.
Percents
15% can also be written as 0.15, or as 15/100 which then must be reduced to 3/20.
How do you Divide FRACTIONS?
Keep, Change, Flip! Then multiply fractions!
Absolute value of a negative number. IxI = -3
NO SOLUTION
Use the structure of an expression to identify ways to rewrite it.
Example: See x^4 - y^4 as (x^2)^2 - (y^2)^2, thus recognizing it as the difference of two squares that can be factored as (x^2-y^2)(x^2+y^2).
Estimate the Rate of Change from a graph
Find the change in y-values, then divide by the change in x-values.
How do you Add and Subtract FRACTIONS?
You have to have a common denominator.
Linear functions
Over equal intervals, the y-values increase by adding or subtracting the same number each time. *Note that the slope in the example would be 3/1= 3
End Behavior
Describes what is happening to the graph overall as the x-values change. As the x-values decrease, does the graph seem to go up or down? As the x-vales increase, does the graph seem to increase or decrease? This represents the end behavior as being positive or negative.
The sum of a rational number and an irrational number is irrational. An irrational number is one that has decimal places that keep going forever such as pi= 3.14......
2 + 3.14.... = 5.14.... and is still an irrational number.
Identify the effects of k on the graph y=f(x)
y=f(x) + k moves the graph up k units or down k units. y=f(x+k) moves the graph right if k is negative OR left if k is positive. Remember this is opposite of what's on the number line. y=k f(x) vertical stretch if k is bigger than 1 and a vertical compression if k is less than 1.
Associative Property
The way numbers are grouped is different, but the result is the same.
Factoring with 2 terms
Factor out the number or variable that all the terms have in common.
Exponential functions y=2^x Where the variable is the exponent.
Over equal intervals, the y-values increase by multiplying or dividing by the same number each time.
How to solve absolute value inequalities?
Once the absolute value bars are on one side of the equal sign, by itself, you work two separate problems (1) Looks exactly the same as the original equation without the absolute value symbols. (2) Is the same on one side, but flip the inequality symbol and make the number negative.
Axis of Symmetry
The equations x=0 is the axis of symmetry for a parabola in standard form.
Rate of Change
Is another name for slope usually used in word problems.
Factoring with 4 terms
Solve by grouping. Group two sets and then factor those two groups.
Sum
Add
y= and f(x)=
These are the same. They can be interchanged with one another. f(x) simply lets you know the equation is a function. Can also be written with other variables like g(x), p(x), etc.
How to rearrange variables to solve for a specific variable.
Solve A=P+PRT for T. You perform the opposite operation on each variable until you get the one you are solving for all by itself. Subtract P, then divide by P and R.
Distributive Property
Multiply a number or variable to everyone inside parenthesis.
Geometric Sequences
There is a pattern in which you multiply or divide by a common number.
The product of a rational number(other than zero) and an irrational number is irrational
(2)(3.14) = 6.28.... (rational)(irrational) = irrational
How to use the Discriminant when solving the Quadratic Formula?
If the discriminant is positive, you will have 2 solutions or x-intercepts. If the discriminant is zero, you will have 1 solution or x-intercept. If the discriminant is negative, you will have No Solution (or really a complex solution (imaginary) in the form (a + bi)
Compound Interest Formula
A=(P+r/n)^nt Common n values are 12=monthly, 4=quarterly, 2=semiannually, 1=annually. t is the time in years.
The sum of two rational numbers is rational. The product of two rational numbers is rational A rational number is any number that can be written as a fraction. Whole numbers are rational numbers because the number 2 can be written as 2/1.
EX: 1/5 + 2/5 = 3/5 EX. 2/3 * 1/3 = 2/9
Completing The Square
Isolate x^2 + bx on one side, move the number to the other side of the equal sign. Take b, divide by 2, then square the result. Add that number to both side. It will then factor into a perfect square.
Explain each step in solving an equation.
You may have to list the steps you performed explaining what you did, step by step. Know how to justify your solutions.
Absolute Value when solving order of operations problems.
Work any math that you need to within the absolute value bars. Then always give the positive of that number as the answer.
Calculate and interpret the average rate of change (symbolically or from a table)
How fast is it changing? Sometimes you find out how much each one changes, then take their average.
How do you Reduce FRACTIONS?
Find one number that you can divide into both the numerator and denominator that is the same number. Then divide them both by that number.
Solid or Dotted Line? Open or Closed Circle?
If it has the line under it (or equal to) it will be a closed circle or solid line.
Product
Multiply
Geometric Sequence
A pattern in which you multiply or divide each term by the same number.
How to solve when written in function notation.
Ex: f(x) = 3x + 4, solve for f(-2). All you do is replace the x with a (-2) and solve. 3(-2) +4 = -2
Communitive Property
With addition and multiplication, it does not matter what order the numbers are written, you still get the same result.
Quadratic Formula
In standard form, ax^2 + bx + c, where a, b, and c (Just the numbers) can be plugged into the quadratic formula to find the x-intercepts, roots, zeros, or solutions.
Section 3
(24 cards)