Graph of a function
A graph is a picture that shows how sets of data are related to each other. When we make a graph of a function, we are showing how its output changes as we vary its input.
For example, on the right is the graph of the function
The input values (x) of the function are plotted across the horizontal (x) axis. The corresponding point on the curve is the value of the function for that input.
Recall that when you square a positive or negative number, the result is always positive. The graph shows this by going upwards (positive) on both sides of zero.
The shape of the graph is a "fingerprint"
The shape of the graph gives us insights about the function, and each function has its own characteristic shape.
For example the shape of the graph above is called a parabola, and it is the shape associated with any function that has x raised to a power (here 2). So you can glance at a curve with that shape an immediately guess the function has its input raised to a power.
Try it yourself
See Graphical Function Explorer. On that page is an applet where you can enter any functions you like and see what they look like plotted as a graph. You can plot up to three functions on the same graph to see how they compare. The instructions are on that page.
An interactive applet that allows you to see the effects of changing the coeeficients in a cubic function using sliders
Interactive demonstration of the graph of the cosine function in trigonometry
Interactive demonstration of the graph of the sine function in trigonometry
Interactive demonstration of the graph of the tangent function in trigonometry
GFE is a free online function graphing tool that allows you to plot up to three functions on the same set of axes. In the functions you can refer to up to four independent variables that are controlled by sliders. The function grapher can plot sinusoidal and other trigonometric functions including sine (sin), cosine(cos) and tan. Similar to a graphing calculator.
How to customize the General Function Explorer (GFE).
An interactive applet that allows you to graphically see the effects of changing the coeficients in a linear function in the form ax+b using sliders
An interactive applet that allows you to graphically see the effects of changing the coeeficients in a linear function in the form mx+b using sliders
Print blank graph paper  Cartesian (rectangular) coordinates
An interactive applet that allows you to see the effects of changing the coefficients in a quadratic function in standard form using sliders
An interactive applet that allows you to see the effects of changing the coefficients in a quadratic function in vertex form using sliders
Where sine waves occur in nature  sound waves, mechanical motion, electronics, radio waves
Analysis of why the function grapher may sometimes produce incorrect results
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