Question

directions: the graph of the rational function ( f ) is shown above. use the graph of ( f ) to answer problems ( 4 - 7 ).

1. ( lim _{x \to 3} f(x)= )

(a) 2
(b) 3
(c) ( -infty )
(d) ( infty )

1. ( lim _{x \to -infty} f(x)= )

(a) 2
(b) 3
(c) ( -infty )
(d) ( infty )

1. ( lim _{x \to 2} f(x)= )

(a) 2
(b) 3
(c) ( -infty )
(d) ( infty )

1. on the interval ( (3, infty) ), the graph of ( f ) is

(a) decreasing at a decreasing rate.
(b) decreasing at an increasing rate.
(c) increasing at a decreasing rate.
(d) increasing at an increasing rate.
test: topics ( 1.7 - 1.11 )
rational functions
created by bryan passwater

Explanation:

Step1: Analyze the graph for question 4

When \(x\) approaches \(3\) from both sides, the \(y -\)value of the function approaches \(2\).

Step2: Analyze the graph for question 5

As \(x\) approaches \(-\infty\), the \(y -\)value of the function approaches \(3\).

Step3: Analyze the graph for question 6

When \(x\) approaches \(2\) from the right - hand side, the \(y -\)value of the function approaches \(\infty\).

Step4: Analyze the graph for question 7

On the interval \((3,\infty)\), the function is increasing (as \(x\) increases, \(y\) increases). The slope of the tangent line to the graph is getting smaller (the rate of increase is decreasing).

Answer:

1. A. \(2\)
2. B. \(3\)
3. D. \(\infty\)
4. C. increasing at a decreasing rate.