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Simon Fraser University
Math 100
Midterm 1- Exam 1
Last Name (print): First Name
Signature: SFU Email ID:
Instructions:
- Do not open this exam until instructed to do so.
- No calculators, notes or books are allowed.
- When presenting a final answer for your solution, calculator-ready expressions will be given full credit.
- Show all your work. No credit will be given for an answer without the correct accompanying work.
- Answer the questions in the space provided. Continue on the back of the pre- vious page if necessary.
Question Mark Maximum
Total 50
- Consider the points A(โ 3 , โ1) and B(โ 1 , 5):
[2 pts] (a) Find the midpoint P of the segment with endpoints A and B.
[2 pts] (b) Determine the distance between A and B.
[4 pts] (c) Give the equation of the circle with diameter the segment from A to B.
- Consider the function f (x) = x^2.
(a) Find the vertex of the parabola given by g(x) = f (x +
[2 pts] 2) โ 2.
[2 pts] (b) Give the equation of the axis of symmetry of the parabola defined by h(x) = โ 3 f (x โ 4).
[2 pts] (c) Which (if any) of f (x), g(x) and h(x) is an even function? Explain
[4 pts] (d) Sketch the graph of h(x).
- Consider the functions f (x) = 25 x โ 4, g(x) =
x^2 โ 9 and h(x) =
x^2 โ 9 x โ 3.
[3 pts] (a) Find the equation of f โ^1 (x).
[2 pts] (b) Find an expression for (f โฆ g)(x).
[3 pts] (c) Find an expression for (gh)(x) and simplify.
[3 pts] (d) Determine the domain of (gh)(x)
- Consider the function:
h(x) =
3 x^2 + 2 if x < 3 x โ 5 if 3 < x โค 20
[1 pts] (a) Evaluate h(5).
[2 pts] (b) Give the domain of h(x).
[2 pts] (c) What is the range of |h(x)|?
