## Precalculus Practice Exam

Part 1 Test 5 Time: 1 hour

1. Given the two points (6,-7) and (3,4), find the following:
• The distance between the two points.
• The midpoint of the two points.
• An equation of the line between the two points.
• An equation of the circle whose diameter is the line between the two points.

2. On inverse functions:
• When does a function have an inverse?
• What is the relationship between the domain and range of a function and the domain and range of its inverse?
• The graphs of a function and its inverse are symmetric to what line?
• Restrict the domain of the function so that its inverse exists.
• If f(x) has an inverse, find .

3. Given the functions , and , find the following.
• Find (f+g)(x).
• Find (fg)(x).
• Find f(g(x)).

4. How do the following graphs differ from the graph of the function f(x)?
Describe the difference in words.
• f(x)+3.
• f(x-4).
• f(x+5)+6.
• -f(x).
• 2f(x).

5. Concerning the following graph of f(x):
• Approximate the interval(s) where the function is increasing?
• Approximate the interval(s) where the function is decreasing?

6. Solve the inequality