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Chapter 1: Problem 90

Determine whether the statement is true or false. Justify your answer. Every function is a relation.

Short Answer

Expert verified
The statement 'Every function is a relation.' is true as every function satisfies the criteria of a relation, but with an additional restriction.

Step by step solution

01

Define a relation

In mathematics, a relation can be understood as a set of ordered pairs. In other words, for a relation, an input value from one set has an association with the output value from another set.
02

Define a function

A function can be thought of as a special kind of relation. In a function, each input value from a set has an association with exactly one output value from another set.
03

Compare the definitions

From the definitions of both a relation and a function, it can be seen that a function is, indeed, a relation since it satisfies the same criteria, but it also has an additional restriction that every input value in the set must correspond with exactly one output value.

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Most popular questions from this chapter

The function \(F(y)=149.76 \sqrt{10} y^{5 / 2}\) estimates the force \(F\) (in tons) of water against the face of a dam, where \(y\) is the depth of the water (in feet). (a) Complete the table. What can you conclude from the table? $$\begin{array}{|l|l|l|l|l|l|}\hline y & 5 & 10 & 20 & 30 & 40 \\\\\hline F(y) & & & & & \\\\\hline\end{array}$$ (b) Use the table to approximate the depth at which the force against the dam is \(1,000,000\) tons. (c) Find the depth at which the force against the dam is \(1,000,000\) tons algebraically.

Find the difference quotient and simplify your Answer: $$f(t)=\frac{1}{t-2}, \quad \frac{f(t)-f(1)}{t-1}, \quad t \neq 1$$

Sketch the graph of the function. $$g(x)=[[x-3]]$$

(a) Write the linear function \(f\) such that it has the indicated function values and (b) Sketch the graph of the function. $$f(-5)=-1, \quad f(5)=-1$$

Use a graphing utility to graph the function. Be sure to choose an appropriate viewing window. $$f(x)=|x-1|$$
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