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Chapter 5: Q 6. (page 267)

If every horizontal line intersects the graph of a function fat no more than one point, fis an鈥�鈥�鈥�鈥�function.

Short Answer

Expert verified

If every horizontal line intersects the graph of a function fat no more than one point, fis a one-to-one function.

Step by step solution

01

Step 1. Definition

The horizontal line test is a method that can be used to determine if a function is a one-to-one function. This means that, for every y-value in the function, there is only one unique x-value.

02

Step 2. Explanation

If every horizontal line intersects the graph of a function fat no more than one point,f is a one-to-one function.

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Most popular questions from this chapter

Solve the equation. Verify your results using a graphing utility.

7x=73

the function f is one-to-one. Find its inverse and check your answer.

f(x)=-3x-4x-2

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

If f(x)=ax+band g(x)=cx+d, then find: -

(a)f鈭�g

(b)g鈭�f

(c)the domain of f鈭�gand g鈭�f

(d)the conditions for whichf鈭�g=g鈭�f

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=3xx+2
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