Fall 2010
Math 1050 Section 3
Exam I
Instructor: Matthew Housley
Name:
UID:
Instructions: You can earn up to 70 points on this exam. Point values
are marked next to each part of each question. No outside notes, scratch
paper or calculators are permitted. The questions begin after the score
sheet.
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Score Sheet:
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Total:
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1. This question deals with the line passing through (2, 6) and (4, 12).
(1) 2 points. Find the slope of a line passing through the points.
(2) 2 points. Write an equation for the line passing through the points.
(3) 2 points. Find the y-intercept of this line.
(4) 2 points. Use the previous parts of this problem to write the equation of the line in slopeintercept form.
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2.
(1) 2 points. Find the slope of the line 3x + 4y = 7.
(2) 3 points. Find the slope of a line perpendicular to the line 3x + 4y = 7.
(3) 3 points. Write an equation for a line passing through the point (4, 0) with the slope you
obtained in the previous part.
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3.
f (x) = |x| + x2 − x4 .
(1) 2 points. Find f (−x) and simplify.
(2) 2 points. Is f (x) an even function, an odd function or neither? Justify your answer.
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4. Start with the function f (x) = x3 . You do not need to simplify your answers.
(1) 2 points. Shift the function 5 units to the right.
(2) 2 points. Reflect the function from the previous part across the y-axis.
(3) 2 points. Shift the function from the previous part down 2 units.
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5.
x2 + 2x − 35
.
x2 − 3x − 10
(1) 5 points. Factor the numerator and denominator of f (x).
f (x) =
(2) 4 points. For which values of x is x2 + 2x − 35 equal to 0? What are the roots of f (x)?
(3) 2 points. Specify the domain of f (x).
(4) 2 points. Simplify f (x) by cancelling common factors.
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6. 3 points. Does the equation y 2 = 3 − x represent y as a function of x? Justify your answer.
7. 4 points. Find the distance between the points (−1, 4) and (2, 9). Find the midpoint on the line
segment connecting these points.
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8. Let f (x) = 7x2 and g(x) = 3x − 4. Compute the following:
(You don’t need to simplify.)
(1) 4 points. f ◦ g(x).
(2) 4 points. g ◦ f (x).
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9. 4 points. Find all solutions to the equation |2x + 4| = 5.
10. 2 points. Multiply out (3x + 1)(2x − 2) and simplify. (Combine like terms.)
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11. 5 points. Find the inverse of f (x) =
2x − 1
.
3x + 7
12. 5 points. Find the x and y coordinates of the vertex for f (x) = x2 + 4x − 7. Find at least two
other points on the graph. Plot the graph of f .
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