MAT101 Final - Set of Real Numbers Interval Notation Region

MAT101 Final

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)

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. ????(????) = 2

1− 3????

????−2

b. ?(????) = 4

5 + 3√x−4

 

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7. Let ????(????) = 2????3 − 8???? and ????(????) = 7????3 − ????2 + 4???? − 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)

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

????(????) = 3????2 − 5???? − 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. ???? = −3, ????(2, −8)

b. ???? = 2

3 , ????(−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. ????(????) = −3(???? + 2)2 + 5

b. ????(????) = ????2 − 3???? − 3

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12. Solve the quadratic equation for the indicated variable

a. ????2 − 3???? = ????2 − 12 ???????????? ????

b. ????2 − 5???? = 3???? ???????????? ????

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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. ????(????) = 5 − 4????, ????(????) = 1 − ????2

b. ????(????) = 4???? + 2????2, ????(????) = √???? + 8

 

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14. Find inverse and check your answers algebraically.

a. ????(????) = 3 − 2√3???? − 9

b. ????(????) = ????−4

2 − 3

c. ????(????) = 9???? − 9