Math 180

Review Test 1 (Limits & Precalculus Review)

Please bring your book to class on review day!!!

In terms of priority, allow more time for the review of limits than for the pre-calculus review. The test will cover approximately 75% limits & continuity and 25% precalc review.

Review of Chapter 1

Limits and Their Properties **** Most Important!! Start with these exercises****

(p. 91)4-6, 11-25 odd, 29-31, 33, 35, 39, 41-45,49-55 odd, 52, 53, 67, 69,

73-77 odd, 83

Answers to even problems from Review Chapter 1:

4)

x / -0.1 / -0.01 / -0.001 / .001 / .01 / .1
f(x) / .2515 / .25016 / .25002 / .24998 / .24984 / .24846

6 a) DNE; b) 0

30)

40) 42) 44) 2

52) Nonremovable discontinuities at x = -3 and 3;

Review of Precalculus:

  1. Identify any intercepts and sketch the graphs of the following. Which of the relations are functions (that is, in which of the following equations is y a function of x)?

a) b) c)

  1. Put the following equation into standard form, find the center and radius and sketch the circle: . Is y a function of x? Explain.
  1. Find the equation of the line for each scenario and graph each line:
  2. Line that passes through points (7, –1), (7,12)
  1. Line with slope = –2 that passes through point (–2, 6)
  1. Line that passes through points (2, 6) and (4, 6)
  1. Line that passes through point (2,4) and perpendicular to the line .
  1. Determine which of the following relations are functions. If the relation is a function, also list the domain and range for the function.

a)b)

c)d)

  1. Determine which of the following relations are functions. If the relation is a function, also list the domain and range for the function.
  2. {(–1, 7), (–2, 7), (3, 6)}
  3. {(–15, 12), (18, 25), (16, 34), (–15, 17), (20, 30), (100, 150)}
  4. {(2, 2), (3, 3), (4, 4), (5, 5), (–1, 2), (–5, 2)}
  1. Determine which of the following relations are functions. If the relation is a function, also list the domain for each function.
  2. b.

c. d.

  1. Graph the following functions and identify the domain and range of each function:

a) b)

  1. Given and and , evaluate the following:

a) b)c)d)

e) f) g)

  1. Convert the following:
  2. to degreesc. 2.8 radians to degrees
  3. 300º to radiansd. 333.2º to radians
  1. List the six trigonometric functions for the angle whose terminal side passes through the point (1, –1).
  1. If , is positive and what is angle ?
  1. Find the set of all points whose distance from 6 is less than 5 units. (Set up the absolute value inequality, solve the inequality and show the result algebraically, graphically and as an interval).

Answer Key for Precalculus Exercises; (NOTE: you can check any graphs using Maple or graphing calculator)

a) x-int: (2,0); y-int: (0, –3)

b) x-int: (5,0); y-int: (0, );

c) x-int: (0,0), (8,0); y-int: (0,0);

  1. Equation: ; Center: (–3, 4); Radius: 5
  1. a) x = 7

b)

c) y = 6

d)

  1. a) not a functionb) yes, function: D: [–3,∞); R: (–∞, 6]

c) not a functiond) yes, function: D: all reals; R: [–20,∞)

  1. a) yes, function D:{–1, –2, 3}; R:{6,7}

b) not a function; input of –15 has two different outputs

c) yes, function D:{–5, –1, 2, 3, 4, 5}; R:{2, 3, 4, 5}

  1. a) yes, function; D: [–6, 6]b) not a function;

c) yes, function; D: all realsd) yes; D: x ≠ 5, –1

  1. a) D: all reals; R: {0, 1, 3}b) D: [–2, ∞); R: (–∞, 2]
  1. a) –4b) c) undefinedd) 7e) f) 3g)
  1. a) 600ºb) c) 160.4ºd) 5.82 radians
  1. 1 < x < 11; (1, 11);

1