Math MidTerm Questions

MAT101 Mid-term

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Name: ______________________________________________________

1. Fill in the chart below:

Set of Real Numbers Interval Notation Region on the Real Number Line

{x | -2 < x < 0}

(-2, 5)

[5, 6)

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2. Find the indicated intersection or union and simplify if possible. Express your answers in interval notation.

a. (5, 8] ∩ (7, ∞)

b. (-∞, 0] U [-1, 2]

c. [-5, -2) ∩ [-2, 5)

3. Write the set using interval notation a. {x | x ≠ -2, 4, 9}

b. {x | -2 ≤ x ≤ 0 or x = 5}

c. {x | x ≤ -4 or x ≥ 4}

MAT101 Mid-term

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d. {x | x ≥ 3 or x ≤ 5}

4. Plot and label the points A(-8, -7), B(2, -5), C(5, 6), D(0, 5), E(0, 0), F(-5, 4), G(2, -5)

5. Using distance formula, find d between a. A(1, 7) and B(5, 2)

MAT101 Mid-term

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b. C(3, 5) and D(-1, -4)

6. Using distance formula, find y and a midpoint of A and B a. A(2, 3)

B(-4, y)

d=10

b. A(1, 6) B(-2, y)

d = 6

7. Which of the following relations describe y as a function of x? explain your reason. a. R1 = {(-2, 1), (2, 4), (-4, 4), (-1, 1), (-2, -5), (3, 5)}

b. R2 = {(-3, 3), (5, 3), (-2, -1), (4, -1)}

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c. 𝑥3 + 𝑦2 = 1 + 𝑦2

d. 1 − 𝑥2 + 𝑦2 = 2 − 𝑥2

8. Find the domain of the following functions.

a. 𝑓(𝑥) = 2

1− 5𝑥

𝑥−4

b. ℎ(𝑥) = 4

5−√x+4

9. Let 𝑓(𝑥) = 5𝑥3 − 3𝑥 and 𝑔(𝑥) = 2 + 3𝑥

4 . Find and simplify expressions for the following

functions.

a. (f + g)(x)

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b. (f – g)(x)

c. (g – f)(x)

d. (fg)(x)

e. (f/g) (x)

10. Find and simplify the difference quotients for the following functions

a. 𝑓(𝑥) = x2 + 3𝑥 − 4

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b. 𝑔(𝑥) = 3

5𝑥2+2

11. Determine if the following functions are even, odd, or neither even nor odd. a. 𝑓(𝑥) = 5𝑥

b. 𝑎(𝑥) = 1

2𝑥2

c. 𝑤(𝑥) = √3 − 𝑥

d. ℎ(𝑥) = 𝑥2 − 𝑥 + 3