||Time: 3 hours
- 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.
- Find the domain and the range of the function .
Answer: Domain: x>10, Range: .
- Find the inverse of the function on the
- Find the midpoint of the line between the points
(2,7) and (5,-5).
Answer: Midpoint: .
- 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.
- Factor the expression completely over the set of
- Find the exact point(s) of intersection of the graphs
Answer: Points of intersection:(4,6) and (-1,1)
- Rewrite the fraction
as a simple fraction in reduced form.
- Find the exact distance between the two points
(5,7) and (7,5).
Answer: distance: .
- What is the slope of a line:
- parallel to 7x-21y+11=0 ?
- perpendicular to the line 7x-21y+11=0 ?
- On what interval(s) is the function increasing?
Answer: interval: .
- Find the maximum value of the function .
Answer: Max value: 20.
- Solve the equation for x.
- 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 ?
Answer: new point: (6,0).
- If and , find . Simplify your answer.
- Solve the equation
Answer: The equation has no solutions. Note that x=-2 is not a solution.
- 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).
- How can you tell from a graph of a function whether the function
Answer: You can tell by using the Horizontal Line Test to make
sure that every horizontal line only intersects the graph at most once.
- 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
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