5 ## BASIC GRAPHSTHE FOLLOWING ARE THE GRAPHS that occur throughout analytic geometry and calculus. The student should be able to sketch them—and recognize them—purely from their shape. It is not necessary to plot points. A constant function Here is the graph of Is a constant function single-valued? Yes, it is, because to each value of A constant function has the form
where The identity function and the absolute value function
In the absolute value function, the Example. a) What is the domain of the identity function? There is no natural restriction on the values of − < Note first that infinity "" is not a number and it is not a place. It is a word, together with a symbol, that we use to mean: There is no limit to the values of Note that we write " b) What is the range of the identity function? The range are those values of − < Parabola and square root function In the parabola The graph of the square root function is related to Note that the square root function is defined only for non-negative values of Also, the symbol refers to one non-negative number called the principal square root. (See Lesson 26 of Algebra, Example 2.)
Problem 1. What is the domain of the function
This function is defined for all values of
As for the range, the lowest value of Problem 2. What is the domain of the square root function, and what is its range?
The square root function is defined only for non-negative values of
As for the range, the lowest value of The cubic function The cubic function is Problem 3. What is the domain of the cubic function, and what is its range?
Domain: −∞ <
Range: −∞ < The reciprocal function When When Similar properties hold when Note, however, that We will go into this more in Topic 18. * Once again, these are the basic graphs. As the student will see, other graphs will be modifications of these. Next Topic: The vocabulary of polynomial functions Please make a donation to keep TheMathPage online. Copyright © 2021 Lawrence Spector Questions or comments? E-mail: teacher@themathpage.com |