Month: May 2017

During the fifteenth week of Foundations of Mathematics and Pre-Calculus, I learned how to use the slope formula to calculate the slope of line segments. Slope is the measure of the steepness of a line. Slope is the ratio of the vertical change over the horizontal change (rise over run). To calculate slope use the slope formula: m= y2 – y1 over x2 – x1 (m stands for slope). Although, if a variable is given rather than a number, find the value of the variable to calculate the missing length by applying the value of the slope. Labeling the y and x values first can help.

Slope Formula: 

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During the fourteenth week of Foundations of Mathematics and Pre-Calculus, I learned how to use Function Notation to determine values. If the function “f” maps an element x in the domain to an element y in the range, you can write f: x -> y. Note: f(x) does not mean f times x. To determine values using Function Notation, a formula must first be given. Once the formula is given, you can determine the x if f(x) is given, or you can determine the value of f(x) if x is given. If f(x) is given, replace it with the variable. If f(x) is not given, but a number that is equal to it, use the formula of the function to determine f(x). You can write a function in the form f(x) = 2x + 1, it also means y = 2x + 1.

Good To Know: 

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During the thirteenth week of Foundations of Mathematics and Pre-Calculus, I learned how to identify functions. Identifying functions is not to difficult, there are only a few things you need to do. The ways to can identify functions are arrow diagrams, ordered pairs, and graphs. On arrow diagrams, if one input is mapped to more than one output, it’s not a function. For ordered pairs, if the input value is repeated, it’s not a function. Finally, for graphs any vertical line that crosses the graph at more than one place, it’s not a function. This method is called the vertical line test. Some things to know first are: input, output, domain, and range.

Mapping Example:

Ordered Pairs Example:

Graph Example:

Which ones are functions?

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During the twelfth week of Foundations of Mathematics and Pre-Calculus, I learned how to represent the relations between two quantities. To represent two quantities, there are six different ways that can be represented. The ways are: in words, a table of values, a set of ordered pairs, a mapping diagram, an equation, or a graph. These diagrams can help you find the independent and dependant variables, as well as the inputs and outputs.  Therefore, these ways can show the relations, then you can determine further values of different numbers. In my opinion the best way to determine relations is using a graph, and then checking your answers by using an equation, but first the table of values for the first set of numbers should be completed.

Different Ways To Represent Relations: 

Example: