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.

    Answer: tex2html_wrap_inline161 .

  2. Find the domain and the range of the function tex2html_wrap_inline163 .

    Answer: Domain: x>10, Range: tex2html_wrap_inline167 .

  3. Find the inverse of the function tex2html_wrap_inline169 on the interval tex2html_wrap_inline171 .

    Answer: tex2html_wrap_inline173 .

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

    Answer: Midpoint: tex2html_wrap_inline175 .

  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.

    Answer: Three gallons need to be added.

  6. Factor the expression tex2html_wrap_inline177 completely over the set of rational numbers.

    Answer: tex2html_wrap_inline179 .

  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.

    Answer: tex2html_wrap_inline185 .

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

    Answer: distance: tex2html_wrap_inline187 .

  10. What is the slope of a line:

  11. On what interval(s) is the function tex2html_wrap_inline197 increasing?

    Answer: interval: tex2html_wrap_inline199 .

  12. Find the maximum value of the function tex2html_wrap_inline201 .

    Answer: Max value: 20.

  13. Solve the equation tex2html_wrap_inline203 for x.

    Answer: tex2html_wrap_inline205 .

  14. If you shift the graph of tex2html_wrap_inline207 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 tex2html_wrap_inline207 ?

    Answer: new point: (6,0).

  15. If tex2html_wrap_inline215 and tex2html_wrap_inline217 , find tex2html_wrap_inline219 . Simplify your answer.

    Answer: tex2html_wrap_inline221 .

  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 tex2html_wrap_inline207 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

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