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Expressing Relations: There are 4 ways we learned to express relations; An equation, graph, ordered pairs, and table of values. 

Equations:

graph: 

ordered pairs: 

table of values: 

cartasien graph: 

Discrete data: points in the graph are not connected. The data is counted rather than calculated, so the data is often put as whole numbers.

Continuous data: points in the graph are connected. The data is calculated, so the points between points could be any real number.

Linear: the line in the graph is straight.

Nonlinear: the line in the graph is bent or curved.

Input: The input in a relation, or x is the independent variable because its value is not effected by another value. The input is always placed on the horizontal axis on any graph

Domain: the values of x on a graph. If the domain is being determined using discrete data, you line up the points on the graph using the x axis, ex. domain:  {2, 3, 4, 6}. If using continuous data, you must include all real numbers between the points, ex.

x intercept: to find the x intercept in a equation, leave x as it is and replace y with the value of 0, then isolate x, ex.

Output: The output in a relation, or y is the dependent variable because its value is dependent on another value. The out put is always placed on the vertical axis on any graph

Range: the values of y on a graph. If the range is being determined using discrete data, you line up the points on the graph using the y axis, ex. range:  {–3, –1, 3, 6}

If using continuous data, you must include all real numbers between the points, ex.

y intercept: to find the y intercept in a equation, leave y as it is and replace x with the value of 0, then isolate y, ex.  

Functions: A function is a relation, but each input only has 1 output. For example, if you plug 2 in a function, you can only get the output of 3, not 5 or 7.

A quick way to determine whether a graph is a function or not, is placing your pencil vertically on the graph and sliding it from one end to the other. if the pencil and line on the graph intersect more than once on any point on the graph, it is not a function and if it does not, it is a function.

There are 5 similar, but different ways we learned to write functions as equations. The different ways you can write them are called notation.

Function notation: f(x)=3+x

mapping notation: f:x—>5x

set notation: {x>8}

Interval notation: [3, 8)

two variables: y=3x+2

This is one of the questions I had trouble with. I had to find the y-intercept of this equation. When finding the y-intercept, you are supposed to input x as 0, because in a y-intercept on an xy graph the x would have to be zero. Here is a picture that shows this,

However, I made the mistake of imputing y as 0, instead of x. Here is the incorrect equation,

The 3x should have cancelled out, instead of the 2x. Here is the correct equation,

To not make this mistake again, I wrote down this multiple times,

X-int = (x,0)

Y-int = (0,y)