## Precalculus Test Out Practice Exam

Part 1 Test 2 Time: 3 hours

1. Find the equation of the line passing through the points (2,7) and (6,-5). Write the answer in the standard form of the line ax+by+c=0, where a, b, and c are integers and a>0.

2. Find the domain and the range of the function .

3. Find the inverse of the function on the interval .

4. Find the midpoint of the line between the points (2,7) and (5,-5).

5. Five gallons of a mixture is 60% water by volume. Determine the number of gallons of water that must be added to bring the mixture to 75% water.

6. Factor the expression completely over the set of rational numbers.

7. Find the exact point(s) of intersection of the graphs of

Answer: Points of intersection:(4,6) and (-1,1)

8. Rewrite the fraction

as a simple fraction in reduced form.

9. Find the exact distance between the two points (5,7) and (7,5).

10. What is the slope of a line:
• parallel to 7x-21y+11=0 ?

• perpendicular to the line 7x-21y+11=0 ?

11. On what interval(s) is the function increasing?

12. Find the maximum value of the function .

13. Solve the equation for x.

14. If you shift the graph of so that it is superimposed on the graph of f(x-5)+3, where will the shift take the point (1,-3) on the graph of ?

16. Solve the equation

Answer: The equation has no solutions. Note that x=-2 is not a solution.

17. If (2,7) is a point on the graph of an even function, name one other point on the graph. If (3,-8) is a point on the graph of an odd function, name one other point on the graph.

Answer: The other point on the even function is (-2,7). The other point on the odd function is (-3,8).

18. How can you tell from a graph of a function whether the function is one-to-one?

Answer: You can tell by using the Horizontal Line Test to make sure that every horizontal line only intersects the graph at most once.

19. Why can't you find the inverse of without restricting the domain?

Answer: Because the graph of f(x) is a parabola, and a parabola is not a one-to-one function on its entire domain.

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Wed Jul 9 11:58:40 MDT 1997