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A graph is a diagram showing the relation between variable quantities. A typical example is a graph of two variables, x and y, each measured along a pair of axes at right angles.
At secondary school, you may be asked to plot graphs. You may be asked to plot straight-line graphs, quadratic graphs or cubic graphs. This involves finding coordinates and plotting these on x-y axes and joining them.
When you get to senior secondary school the knowledge of graphs is important in topics like the application of differentiation and integration and problems that you will need to quickly sketch graphs for a better understanding.
Types of graphs include different types of straight and curved graphs.
Here we are going to discuss and distinguish between the main types of graphs you will come across in secondary school mathematics.
Straight Line Graphs:
Straight line graphs are graphs of linear functions and are of the form:
\( \scriptsize y = mx\:+\: c\)
Where m is the gradient and c is the y-intercept (where the line crosses the y-axis).
The graphs look like this:
Quadratic Graphs:
Quadratic graphs are graphs of a quadratic function and can be recognised as they include a squared term. e.g. x2. The shape of the graph is a parabola.
A parabola is a curve in the shape of a U or an upside-down U.
A quadratic graph has one turning point – a minimum point or a maximum point.
The turning point of any curve or parabola is the point at which its direction changes from upward to downward or vice-versa.
The graphs look like this:
Cubic Graphs:
Cubic graphs are graphs of a cubic function and can be recognised as they include a cubed term. e.g. x3. Cubic graphs are s-shaped.
Cubic graphs often have two turning points – a minimum point and a maximum point
Exponential Graphs:
This type of graph starts as a horizontal line then increases/decreases slowly and then grows/decays rapidly. They are graphs of an exponential function and can be recognised as they include a kx term where k is the base and x is the exponent (power).
The graph can be a growth curve that starts as a horizontal line then increases slowly, and then grows rapidly. Here k is greater than 1. e.g. \( \scriptsize y = 2^x\)
The graph can be a decay curve that decreases slowly and then decays rapidly. Here k is less than 1. e.g. \( \scriptsize y = 0.2^x\)
More complex exponential curves are of the form: \( \scriptsize y = ab^x\)
Being able to identify and sketch graphs is very useful in solving mathematical problems involving graphs.
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