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Jan 26, 2023 · Types of Graphs. Why do we need to know what graphs look like? Graphs are used in various aspects of mathematics – but in the real world they can take on specific meanings. For example a linear (straight line) graph could be the path a ship needs to sail along to get from one port to another.
- Quadrants of A Graph
- Plotting Graphs
- Types of Graphs
- X to The Power of 1
- X to The Power of 2
- X to The Power of 3
- Drawing Graphs by Hand
- Linear and Non-Linear Graphs
- Linear Or Non-Liner Equations
- Interpolation
In mathematics, it is common to represent data from situations. This is often done with the use of a graph which is a great way to show two different measurements against each other (for example, the graphs we have previously looked at that compared speed and time). A normal graph can be split into four different sections depending on the values of...
In order to plot a graph we simply need to have values for different things. These could be anything at all and we must plot one on the horizontal (x) axis and the other on the vertical (y) axis. Each point can then be joined up or inspected to see a trend between the two things we are measuring. This will allow us to make future predictions or rep...
There are many different types of graphs that we can get using line equations. Which one we have will depend on the individual equation and the power of the x or y variable. From now on we will assume that the equation is separated and y is made to be the subject on the left-hand side. The types of graph that we will get will be one of the followin...
This will always result in a line and not a curve. An example of a line like this will have an equation of or any other combination as long as is not to any power. This looks like:
When is x squared we get a curve which has either a minimum or maximum (a specific largest point or smallest). So we get a curve which looks like either a u-shape or an n-shape. This looks like:
When x is cubed we get a curve which changes direction twice. This can be in either direction such as the images shown below. This looks like: All of these graphs could be slightly different in the way they look in terms of steepness and other aspects, the only thing which must stay the same is the number of times the curve changes in comparison to...
When drawinga graph by hand we must follow certain steps. Firstly, we need to find some of the individual points that lie on the curve by choosing certain values of x and finding the corresponding y. When doing this you should look to find at least five points to give a good idea of where the curve will be. You should remember how many times the cu...
Graphs can be used even when we have continuous data, meaning that the numbers used can be absolutely anything and are not just whole numbers. Another advantage of a graph is that we can easily compare two things directly to one another; this then gives us a great tool to help us have an effect on the two different outcomes as we will know what sor...
When we plot a graph we can have one of two types: linear or non-linear. A linear graph basically means that when plotted we will see a straight line, hence the word linear meaning ‘line like’. Obviously, a non-linear graph will give us a curved shape when plotted. The way to spot the difference when we are just given the equations for a line is to...
As we mentioned earlier, one of the things with graphs is that the numbers involved can be anything. This obviously gives us a problem when plotting graphs as we will not wish to waste time plotting every single individual point. For this reason, we use interpolation to plot a graph. This means that we simply have to mark a few points that are corr...
In order to use different types of graph to solve an equation: Add a line to the coordinate grid. See where the line crosses the curve. Draw a straight vertical line from the curve to the x -axis. Read off the value on the x -axis.
Nov 16, 2022 · Definition 1. Given the function f (x) f (x) then. f (x) f (x) is concave up on an interval I I if all of the tangents to the curve on I I are below the graph of f (x) f (x). f (x) f (x) is concave down on an interval I I if all of the tangents to the curve on I I are above the graph of f (x) f (x).
Nov 16, 2022 · In this section we will discuss what the first derivative of a function can tell us about the graph of a function. The first derivative will allow us to identify the relative (or local) minimum and maximum values of a function and where a function will be increasing and decreasing.
Jul 21, 2022 · Two points on a plane determine a line. A line is a one-dimensional figure that is made up of an infinite number of individual points placed side by side. In geometry, all lines are assumed to be straight; if they bend they are called a curve. A line continues infinitely in two directions.
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Nov 10, 2020 · The graph of parametric equations is called a parametric curve or plane curve, and is denoted by \(C\). Notice in this definition that \(x\) and \(y\) are used in two ways. The first is as functions of the independent variable \(t\).
