Functions and Their Graphs IP

MTH133

Unit 4 - Individual Project - A

Name

1 ) State the domain of the following Answer : [-4 Answer (- , 3 (3 Answer (- Answer (- Answer (-

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

a

Answer : g (x x2 - 3 b

Answer : g (x (x - 4 )2

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 (x 2 )2 -3

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

Answer : h -2 Show your work here : Function f (x ) can be rewritten in the following way

f (x x2 4x 1

f (x x2 4x 4 - 3

f (x (x2 4x 4 ) - 3

f (x (x 2 )2 - 3 Hence the x-coordinate of the vertex of this parabola is -2

b ) Substitute the two integers 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 equations of the horizontal and vertical asymptotes for the following . Type if the function does not have an asymptote Answer

Horizontal : y 2

Vertical : x -2 Answer

Horizontal : y 0

Vertical : --- (absent

c

Answer

Horizontal : y 2

Vertical : x -2

d

Answer

Horizontal : y 0

Vertical : x 1

P...