Math 101: Precalculus 1
Fall 2016
Midterm Review
Test date: October 4, 2016
No textbooks, notes, or other outside resources are allowed.
Calculators (no phones, iPads, or computers) are permitted, but please show all work in provided
space. Answers without work will receive minimal credit.
1. Let f (x) = 12 x3 + 2.
(a) Identify the parent function and sketch its graph.
Parent function:
(b) List the transformations in order and sketch the graph at each step.
(You may not need all of the provided graphs.)
#1:
#2:
#3:
Math 101: Precalculus 1
Midterm Review - Page 2 of 6
2. (a) Determine the domain of f (x) =
October 4, 2016
p4x .
x 1
Domain:
(b) Determine the domain and range of g(x) given by the graph.
Domain:
3. Let f (x) =
Range:
2x
6 x.
(a) Find the inverse of f (x).
(b) Determine the domain and range of f (x) and f
Domain of f :
Domain of f
1 (x).
Range of f :
1:
Range of f
1:
Math 101: Precalculus 1
Midterm Review - Page 3 of 6
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4. For each function, determine if it is one-to-one. If the function is not one-to-one, truncate the
domain so that it is one-to-one.
(a) f (x) = 4x2 , x 
One-to-one?
1
New domain (if needed):
(b) f (x) = |3x|
One-to-one?
New domain (if needed):
(c) f (x) =
One-to-one?
New domain (if needed):
(d) f (x) =
One-to-one?
New domain (if needed):
5. Find an equation of the parabola with vertex ( 5, 2) and containing the point ( 1, 6).
Math 101: Precalculus 1
6. Let f (x) = x2
Midterm Review - Page 4 of 6
7x + 6. Determine the following and use your answers to sketch the parabola.
(a) Opening direction:
(b) Vertex:
(c) y-intercept:
(d) x-intercepts:
(e)
7. Let f (x) = 12 x2 + 4 and g(x) =
(a) (f + g)(x) =
(b) (f g)(3) =
(c) (f
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g)(x) =
(d) (g f )( 2) =
1
1 x
and determine the following.
Math 101: Precalculus 1
Midterm Review - Page 5 of 6
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8. Match each description to a line it describes. Note not all graphs will be described.
(a) A line perpendicular to y = 4x
3.
(b) A line with satisfying the equation 6x
(c) A line with slope m =
1
2
2y = 4.
and y-intercept at y =
3.
9. For each pair f (x) and g(x), determine if they are inverses. Justify your answer.
(a) f (x) =
(b)
p
x + 1 and g(x) = x2
1
Math 101: Precalculus 1
Midterm Review - Page 6 of 6
10. Consider the points ( 6, 4) and (3, 2) and calculate the following.
(a) Midpoint
(b) Distance between the points
(c) Slope of the line containing both points
11. The graph of f (x) is given below.
(a) Determine the intervals on which f (x) is
i. Increasing:
ii. Decreasing:
iii. Constant:
(b) Give the points of any
i. Relative maximums:
ii. Relative minimums:
(c) Determine if f (x) is odd, even, or neither. Explain your reasoning.
12. For f (x) = 3x
4 and g(x) = x2
(a) Solutions to f (x) = g(x)
(b) Zeroes of g(x)
2, find the following.
October 4, 2016