```Math 1050-1
Name:
Exam 1
ST#
calculator, notes, or any other electronic devices. Unless specified you do not need to simplify
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1. (5 pts) Completely simplify the following:
x2 −9
5x
x2 −5x+6
10x2
2. (5 pts) Steve is competing in a race. The course is in the shape of a right triangle with checkpoints at
the vertices. The first leg of the course is uphill and in a Northwest direction. Steve runs at a speed
of s, and gets to the first check station after 2 hours. The second leg of the race is downhill and in a
Northeast direction. He runs 5 miles per hour faster then his beginning speed, and gets to the second
checkpoint after 1 hour. The last leg of the race is 9 miles. How fast did Steve run uphill?
Second Check Station
First Check Station
Start and Finish Line
3. Consider the function f (x) =
r
9−
9 2
x .
25
(a) (7 pts) What are the x and y-intercepts. Make sure each of your answers is a point.
(b) (3 pts) What kind of symmetry, if any, does the graph of this function have? You must give some
(c) (3 pts) What is the domain of the function?
(d) (2 pts) Evaluate f (0) and f (5).
(e) (3 pts) Graph the function.
y
6
5
4
3
2
1
0
x
−1
−2
−3
−4
−5
−6
−6
−5
−4
−3
−2
−1
0
1
2
3
4
5
6
4. Consider the equation 3y = −5x + 8.
(a) (5 pts) What is the equation of the line perpendicular to the given line which passes through the
(b) (5 pts) Where do the two lines intersect?
5. Refer to the graph below to answer the following questions.
4
y
2
–4
–2
0
2
4
x
–2
–4
(a) (2 pts) Is this the graph of a function? Explain why or why not.
(b) (2 pts) Does this graph have an inverse function? Explain why or why not.
(c) (4 pts) Identify where the graph is increasing, decreasing, or constant.
6. Below is the graph of g(x) = −x2 + 4x + 1.
8
6
y
4
2
–6
–4
–2
0
2
4
6
x
–2
–4
–6
–8
(a) (5 pts) Find the average rate of change between x1 = 3 and x2 = 4.
(b) (3 pts) What is the equation of the secant line between x1 and x2 ? Leave your equation in
point-slope form.
7. Consider the equation g(x) = −(x + 3)3 − 2.
(a) (3 pts) Describe the vertical shifts, horizontal shifts, and reflections of this graph as compared to
the function f (x) = x3 .
(b) (3 pts) Graph g(x).
8
7
6
5
4
3
2
1
0
−1
−2
−3
−4
−5
−6
−7
−8
−4
−3
−2
−1
0
1
2
3
4
8. (5 pts) Given f (x) = 3x + 5 and g(x) = 2x2 − 7x + 9, find the following. Do not simplify your answers.
(a) (f − g)(x)
(b) (g ◦ f )(x)
9. (5 pts) Find the inverse of the function f (x) =
3x + 4
.
5x
```