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Chapter 2: Q. 10 (page 68)

True or False Every relation is a function.

Short Answer

Expert verified

The given statement is false.

Step by step solution

01

Step 1. Given information 

In the given question we have to explain the given statement is true or false.

The statement is "Every relation is a function."

02

Step 2. Definition of Relation and Function 

Relation-The relation is defined as the collection of ordered pairs, which contains an object from one set to the other set.

Functions-The relation that defines the set of inputs to the set of outputs is called the functions. In function, each input in the set X has exactly one output in the set Y.

03

Step 3. All functions are relations but all relations are not functions.

Hence, the given statement is false.

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Most popular questions from this chapter

A wire of length xis bent into the shape of a circle.

Part (a): Express the circumference Cof the circle as a function of x.

Part (b): Express the areaAof the circle as a function ofx.

An island is 2 miles from the nearest pointP on a straight

shoreline. A town is 12 miles down the shore from P. See the

illustration.

(a) If a person can row a boat at an average speed of 3 miles per hour and the same person can walk 5 miles per hour, build a model that expresses the time Tthat it takes to go from the island to town as a function of the distance x from P to where the person lands the boat.

(b) What is the domain of T ?

(c) How long will it take to travel from the island to town if

the person lands the boat 4 miles from P?

(d) How long will it take if the person lands the boat 8 miles

from P ?

Determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find: (a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, the y-axis, or the origin.

True or False The domain and the range of the reciprocal function are the set of all real numbers.

Inscribe a right circular cylinder of height h and radius r in a cone of fixed radius Rand fixed height H. See the illustration. Express the volume V of the cylinder as a function of r.

[Hint: V=蟺谤2h. Note also the similar triangles.]
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