College Algebra

MTH133

Unit 4 - Individual Project - A

Name

1 ) State the domain of the following and provide a brief explanation for your answer Answer : - 4 ( x Answer : - x Answer : - x x Answer : - x

2 ) Suppose the graph of y x2 is shifted to obtain each the following graphs . What is the equation of the function , g (x , for each graph Write your answers in terms of x2 and /or x

a

Answer : y x2 - 3

b

Answer : y (x - 4 )2 p

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 . The present coordinates of

is (1 0

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 (-2 , -3

Show your work here : According to Stroud 's Engineering Mathematics , the vertex of a parabola is either the minimum or the maximum value of the function . At any of this points , the slope is zero and as a result the derivative of the function at either of this two points assumes the value of zero . That is , dy /dx 0 . For the function in the question

dy /dx 2x 4 0

And , 2x -4

x -2

When x -2 , y f (x (-2 )2 4 (-2 1 -3...