Functions and Their Graphs

MTH133

Unit 4 - Individual Project - A

Name

1 ) State the domain of the following Answer : x ? -4 Answer : All real number excluding x 3 (x ? 3 Answer : All real number Answer : All real number Answer : All real number

is shifted to obtain each the following graphs . What is the equation of the function , g (x , for each graph

a )b 3 ) Consider the following graph of y f (x

a ) If h (x f (x 2 , what would the new coordinates of

be after the shift

? Give answer in (x , y ) form

Answer (1 , 2 , what would the new coordinates of

be after the reflection ? Give answer in (x , y ) form

Answer (-1 , 0

a ) Find h , the x-coordinate of the vertex of this parabola Answer : h -2

Show your work here h - (b /2a - (4 /2 -2

Or alternatively ( h -2

b ) Substitute the two whole number values immediately to the left and right of h into the function to find the corresponding y . Fill in the following table . Make sure your x-values are in increasing in your table

Answer

x y

-4 1

-3 -2

h -2 -3

-1 -2

0 1 c ) Use MS Excel to graph the function by plotting the points found in the table in part b

Answer

5 ) Find the horizontal and vertical asymptotes of the following . Type if the function does not have an asymptote Answer

Horizontal : y 2

Horizontal asymptote at y (numerator 's leading coefficient (denominator 's leading coefficient 2x /x 2 [the degrees of numerator and denominator are same]

Vertical : x -2

Putting denominator x 2 0 ( x -2 Answer

Horizontal : y 0 (x-axis

The denominator (for x ) degree is greater then numerator degree by one therefore , horizontal asymptote will be y 0

Vertical : -

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J

K

O

Q

q

r

s

t

u

v

B

X

u

yo

No

A

d

zh

3

A

B

C

V

X

Y

l

B

B ?m

n

o

p

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B ?i ?h ?Denominator (x^2 1 0 , have no real solution

c

Answer

Horizontal : y 2

Vertical : x -2

d

Answer

Horizontal : y 0 (x-axis

Vertical : x 1

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