College Math Exam

MAT101 Final

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Name: ______________________________________________________

1. Fill in the chart below:

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

{x | -1 ≤ x < 0}

[-3 2]

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

a. [2, 8] ∩ (7, ∞)

b. (-9, 4] U [-1, 2]

3. Write the set using interval notation a. {x | -6 ≤ x ≤ 5 or x = 9}

b. {x | x ≥ -2 or x ≤ 9}

4. Using distance formula, find d between A(3, √7) and B(2, -9)

MAT101 Final

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5. Using distance formula, find y and a midpoint of A and B a. A(5, 2)

B(-4, y)

d=7

6. Find the domain of the following functions.

a. 𝑓(𝑥) = 2

1− 3𝑥

𝑥−2

b. ℎ(𝑥) = 4

5 + 3√x−4

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7. Let 𝑓(𝑥) = 2𝑥3 − 8𝑥 and 𝑔(𝑥) = 7𝑥3 − 𝑥2 + 4𝑥 − 2. Find and simplify expressions for the following functions.

a. (f + g)(x)

b. (f – g)(x)

c. (g – f)(x)

d. (fg)(x)

e. (f/g) (x)

MAT101 Final

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8. Find and simplify the difference quotients for the following function of

𝑓(𝑥) = 3𝑥2 − 5𝑥 − 3

9. Find both the point-slope form and the slope-intercept form of the line with the given slope

which passes through the given point

a. 𝑚 = −3, 𝑃(2, −8)

b. 𝑚 = 2

3 , 𝑃(−2, 2)

10. Solve the each of the following equations

a. |2x + 3| = 9

b. 2 - 4|x – 7| = -14

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11. Find x- and y-intercepts, if any exists. Convert general form into standard and standard into

general form. Find the domain, and range, and identify the vertex and the axis of symmetry.

a. 𝑓(𝑥) = −3(𝑥 + 2)2 + 5

b. 𝑓(𝑥) = 𝑥 2 − 3𝑥 − 3

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12. Solve the quadratic equation for the indicated variable

a. 𝑦2 − 3𝑦 = 𝑥 2 − 12 𝑓𝑜𝑟 𝑥

b. 𝑦2 − 5𝑦 = 3𝑥 𝑓𝑜𝑟 𝑦

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13. Use the given pair of functions to find the following values if they exist

(g○f)(2) (f○f)(-3) (f○g)(-2) (g○g)(8)

a. 𝑓(𝑥) = 5 − 4𝑥, 𝑔(𝑥) = 1 − 𝑥 2

b. 𝑓(𝑥) = 4𝑥 + 2𝑥 2, 𝑔(𝑥) = √𝑥 + 8

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14. Find inverse and check your answers algebraically.

a. 𝑓(𝑥) = 3 − 2√3𝑥 − 9

b. 𝑓(𝑥) = 𝑥−4

2 − 3

c. 𝑓(𝑥) = 9𝑥 − 9