Exercises for Question Type 2: Graphing functions for different pairs of a,b,c in (x+a)/(x+b)(x+c) to test different looks of graphs

Question 1

Specification

Consider the function f (x) = \frac{x + 1}{( x - 1 ) ( x + 1 )} . Determine the domain, any holes, asymptotes, intercepts, and end behavior. Hence, sketch the graph of f .

[9]

Question 2

For f (x) = \frac{x}{( x + 2 ) ( x + 3 )}, determine its domain, asymptotes, intercepts, end behavior, and sketch via technology.

[7]

Question 3

Consider the function f (x) = \frac{x + 2}{( x + 2 ) ^{2}} . Find the domain, holes, asymptotes, intercepts, and end behavior of the function. Sketch the graph of f using technology.

[7]

Question 4

Analyze and graph f (x) = \frac{x - 2}{( x + 1 ) ( x + 4 )} : find domain, asymptotes, intercepts, end behavior, and sketch using technology.

[5]

Question 5

For the function f (x) = \frac{x + 6}{( x + 2 ) ( x + 3 )}, determine its domain, vertical and horizontal asymptotes, intercepts, end behavior, and sketch its graph using technology.

[8]

Question 6

Sketch the graph of f (x) = \frac{x - 5}{( x - 3 ) ( x + 1 )} . Clearly state the equations of any asymptotes, the coordinates of any axes intercepts, and the domain.

[7]

Question 7

Sketch f (x) = \frac{x + 1}{( x + 2 ) ( x + 3 )} by finding its domain, asymptotes, intercepts, end behavior, and using technology for the graph.

[8]

Question 8

The function f is defined by f (x) = \frac{x + 5}{( x + 5 ) ( x + 1 )} .

(a)

State the domain of f .

[1]

(b)

Find the coordinates of the hole on the graph of f .

[3]

(c)

Write down the equation of the vertical asymptote and the equation of the horizontal asymptote.

[2]

(d)

Find the coordinates of the y -intercept and explain why there is no x -intercept.

[2]

(e)

Sketch the graph of f, clearly showing the hole and the asymptotes.

[2]

Question 9

Analyze and graph f (x) = \frac{x + 6}{( x - 2 ) ( x + 4 )} : find the domain, asymptotes, intercepts, end behavior, and sketch the graph using technology.

[7]

Question 10

(a)

Consider the function f (x) = \frac{x + 2}{( x - 1 ) ( x + 3 )} . Find the domain, the coordinates of the axes intercepts, and the equations of any asymptotes of the function f (x) .

[5]

(b)

Sketch the graph of f, clearly showing the asymptotes and intercepts.

[3]

Question 11

Determine the graph of f (x) = \frac{x - 3}{( x + 1 ) ( x - 2 )} : find domain, asymptotes, intercepts, end behavior, and sketch with technology.

[8]

Question 12

Sketch f (x) = \frac{x + 4}{( x + 2 ) ( x - 3 )} after finding its domain, vertical and horizontal asymptotes, intercepts, end behavior, and graphing with technology.

IB Mathematics Analysis and Approaches Question Type 2: Graphing Functions for Different Pairs of A,b,c in (x+a)/(x+b)(x+c) to Test Different Looks of Graphs Exercises