College Algebra

MTH133

Unit 4 - Individual Project - A

Name

1 ) State the domain of the following Answer : x ? -4 (All real number greater than -4 , including -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 For parabola 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 (Since , the degrees of numerator and denominator are same , therefore horizontal asymptote at y (numerator 's leading coefficient (denominator 's leading coefficient 2

Vertical : x -2 (Putting x 2 0 for vertical asymptote Answer

Horizontal : y 0 (x-axis (Since , the denominator 's degree is greater then numerator 's by one therefore , a horizontal asymptote at y 0

Vertical (since x^2 1 0 , have no solution

c

Answer

Horizontal : y 2

Vertical : x -2

d

Answer

Horizontal : y 0 (x-axis

Vertical : x 1

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