1. Determine analytically if the following functions are even, odd or neither.
3
2
a. f(x) = x + x + x + 1 b. f(x) = √ √ 1−x 2 Answers: a. neither b. even
2. Use the graph of y = f(x) given below to answer the questions. f(x)
6
4
2
-5 -4 -3 -2 -1 0 0 1 2 -2
-4
-6 a. Find the domain of f.
b. Find the range of f.
c. Determine f(2).
d. Solve f(x) = −5.
Answer: a. [−4, 4] b. [−5, 5) c. f(2)=3 d. x= -2 3 4 5 3. Sketch the graph of the given function. State the domain of the function,
identify any intercepts and test for symmetry
2
a. f(x) = x + 1 b. f(x) = x(x − 1)(x + 2) Answer: a. Domain: (−∞, ∞) x-intercept: None y-intercept: (0, 1) Even
b. Domain: (−∞, ∞) x-intercepts: (−2, 0), (0, 0), (1, 0)
y-intercept: (0, 0) No symmetry 4. 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 = −1, P(−7, −1) b. m = 678, P(−1, −12) Answer: a. y + 1 = −(x + 7) y = −x – 8 b. y + 12 = 678(x + 1) y = 678x + 666 5. You are given a line and a point which is not on that line. Find the line
perpendicular to the given line which passes through the given point.
a. y = −6x + 5, P(3, 2) b. y = 6, P(3, −2) Answer: a. y = 1/ 6 x + 3/2 b. x = 3 6.Solve the equation :
a. 2|5x + 1| − 3 = 0 b. |2x − 1| = x + 1 Answer: a. x = − 1 /2 or x = 1/ 10 b. x = 0 or x = 2 7. Determine whether or not the equation represents y as a function of x.
a. x2 − y2 = 1 b. . y = x2 + 4 Answer : a. Not a function b. Function 8. Use the pair of functions f and g to find the following values if they exist.
(f + g)(2) (f − g)(−1) (g − f)(1) a.f(x) = 3x + 1 and g(x) = 4 – x (fg) (1/ 2) (f/ g) (0) b. f(x) = √ x √ x+3 2
2
c.f(x) = x − x and g(x) = 12 − x ( g/ f) (−2) and g(x) = 2x – 1
1 2
d. f(x) = x + 1 and g(x) = x 2 +1 9. Let f be the function defined by
f = {(−3, 4),(−2, 2),(−1, 0),(0, 1),(1, 3),(2, 4),(3, −1)}
and let g be the function defined by
g = {(−3, −2),(−2, 0),(−1, −4),(0, 0),(1, −3),(2, 1),(3, 2)} .
Compute the indicated value if it exists:
a. (f + g)(−3) b. (f − g)(2) Answer: a.(f + g)(−3) = 2 b. (f − g)(2) = 3 c. (fg)(−1)
c. (fg)(−1) = 0 d. (g + f)(1)
d. (g + f)(1) = 0

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