Answer Horizontal asymptote = y = 2 Vertical asymptote = x = 3 Explanation Given : The function is : g ( x ) = 2 x x − 3 Calculation: Make a table of different values of function: x g ( x ) = 2 x x − 3 6 4 1 -1 x → 3 + g ( x ) = 2 x x − 3 → + ∞ x → 3 − g ( x ) = 2 x x − 3 → − ∞ x → + ∞ g ( x ) = 2 x x − 3 → 2 x → − ∞ g ( x ) = 2 x x − 3 → 2 Plot the points and we get the graph of the function. An asymptote is a value of a function that you can get very near to, but you can never reach. So, the function has two asymptotes: Horizontal asymptote = y = 2 Vertical asymptote = x = 3

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5.4, Problem 5E

To determine

Graph each function. Show any asymptotes as dashed lines.

Expert Solution & Answer

Answer to Problem 5E

Horizontal asymptote = y=2

Vertical asymptote = x=3

Explanation of Solution

Given :

The function is :

g(x)=2xx−3

Calculation:

Make a table of different values of function:

x	g(x)=2xx−3
6	4
1	-1
x→3+	g(x)=2xx−3→+∞
x→3−	g(x)=2xx−3→−∞
x→+∞	g(x)=2xx−3→2
x→−∞	g(x)=2xx−3→2

Plot the points and we get the graph of the function.

Algebra and Trigonometry: Structure and Method, Book 2, Chapter 5.4, Problem 5E

An asymptote is a value of a function that you can get very near to, but you can never reach.

So, the function has two asymptotes:

Horizontal asymptote = y=2

Vertical asymptote = x=3

Chapter 5.4, Problem 4E

Chapter 5.4, Problem 6E

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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