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Chapter 1: Problem 2

Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(4,5),(6,7),(8,8)\\}$$

Short Answer

Expert verified
Yes, the relation is a function. The domain is \(D=\{4,6,8\}\) and the range is \(R=\{5,7,8\}\).

Step by step solution

01

Verify if the relation is a function

The relation given is \\{(4,5),(6,7),(8,8)\\}. Looking at each pair, it can be seen that each x-value is linked to exactly one y-value, hence this relation is indeed a function.
02

Determining the domain and range

For domain, list all distinct x-values from the ordered pairs. The x-values are 4, 6, and 8. So, the domain is \(D=\{4,6,8\}\). For range, list all distinct y-values from the ordered pairs. The y-values are 5, 7, and 8.Therefore, the range is \(R=\{5,7,8\}\).

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Most popular questions from this chapter

Determine whether each relation is a function. Give the domain and range for each relation. a. \(\\{(1,6),(1,7),(1,8)\\}\) b. \(\\{(6,1),(7,1),(8,1)\\}\) (Section \(1.2,\) Example 2 )

Explaining the Concepts: If equations for \(f\) and \(g\) are given, explain how to find \(f-g .\)

How is the standard form of a circle's equation obtained from its general form?

Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}-2 x+y^{2}-15=0$$

Use a graphing utility to graph each function. Use \(a[-5,5,1]\) by [-5,5,1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing, or constant. $$f(x)=x^{\frac{1}{3}}(x-4)$$
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