Chapter 5. Graphs

OBJECTIVES

When you have completed this chapter, you should be able to

  • Graph a table of point pairs or an empirical function.

  • Graph any function given in explicit form.

  • Graph some functions given in implicit form.

  • Graph a relation.

  • Use the graphing calculator to make a complete graph of a function.

  • Find the slope of a straight line.

  • Graph a straight line given its slope and y-intercept.

  • Write the equation of a straight line, given its slope and y-intercept.

  • Write the equation of a line given two points on the line.

  • Solve equations graphically.

It's said that "a picture is worth a thousand words," and in this chapter we will show how to make a picture of an equation, that is, how to draw a graph. After introducing the rectangular coordinate system, we will plot points, and then data derived from an experiment. We will go on to graph functions and relations, given in both explicit and implicit form, first manually, and then with the graphing calculator. The idea of a complete graph will be stressed.

Next we will examine the straight line in more detail, giving a quick way to graph it given the equation, and to find its equation, given some information about the line.

Finally covered are methods to approximately solve any equation graphically. This is very important because many equations cannot be solved in any other way.

There will be more on graphing later. For example, we will draw other kinds of graphs in our chapter on statistics: bar charts, pie charts, scatter ...

Get Technical Mathematics, Sixth Edition now with the O’Reilly learning platform.

O’Reilly members experience books, live events, courses curated by job role, and more from O’Reilly and nearly 200 top publishers.

Start your free trial