Math 151 Fall 04.

Test 1 (show all your works) Print Name MWF: 9 or 10 or 12.

1. (30 points) Let

1. Find the function so that the graph of is being reflected along [hint:

2. Find the function so that the graph of is being shifted to the right units and down units from [hint:

3. Find the inverse function for and graph the inverse function together with [hint: find the inverse using the followings:

• the inverse for is

• the inverse for is

• the inverse for is

• the inverse for is

• the inverse for is

2. (10 points) Find two rational functions which satisfy ALL the following conditions: [hint: try and

1. the vertical asymptotes of are at and ;

2. the horizontal asymptote of is at ;

3. .

3. (10 points) If ,

1. find the horizontal and vertical aysmptotes of , [hint: h.a. is and v.a. are and

2. solve [hint: graph first and solve

4. (20 points) Find a function whose graph (shape) could resemble the following. Note the are at and [hint: try

5. (10 points) If the graph of a function is given in the first quadrant. Then label the remaining functions ,, whose graphs are given below.

6. (15 points) If

1. find the vertical asymptote of [hint: since has the v.a. and is being shifted to the right so the v.a. for is

2. find (the inverse function of [hint: the inverse for is so

3. find [hint:

7. (15 points) Let Then

1. find the vertex of this parabola, [hint:

2. sketch the graph of

3. find the domain and range for [hint: domain is and the range is ]