Tools on Math Open Ref make it very easy to explore a variety of graphs. Try these which can all be displayed full screen:
Linear Functions Explorer
Note the links to the other graph explorers – Quadratic, Cubic and General Function.
Use any of the free online graph plotters to explore a variety of lines and curves.
See also this post to Explore Straight Lines and learn more about the Desmos graphing calculator.
To explore the different graphs you should be familiar with for GCSE (age 14-16) use the text links on each slide:
This is also available as a pdf. Desmos Graphs GCSE.
The pdf should also display well on a phone.
Tools such as these allow you to study transformations and graphs – for example you could show
y=x2 y=(x-2)2 and y=x2+3 on the same diagram.
Click on the above image to see the graphs on the Desmos Graphing Calculator.
You can easily set up the Desmos Graphing Calculator to include sliders.
The value you assign to a variable determines the values the variable can take – you can easily change the value by typing a new one – or click on the numbers at either end of a slider to change them.
Suppose you want to explore quadratic curves. (Click on the image).
or perhaps you wish to explore cubic curves:
Further examples (click on each image for a Desmos page
Direct link to presentation on Slideshare.