### Determine if each function is even, odd or neither. Show all work and include an explanation of any symmetry that exists

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A+ TUTORIAL FOR THE FOLLOWING QUESTIONS

**Operations on Functions**

Mid-Unit Assignment

Operations on Functions Mid-unit Assignment

1.Determine if each function is even, odd or neither. Show all work and include an explanation of any symmetry that exists. (7 marks)

a.y = x4 + 4x2

b.y = 3x3 - x - 3

c.y = x5 - x3 + x

d.y = 3

2.In the graph below, f(x) is the parabola and g(x) is the straight line. Sketch a graph of f + g and f g. Put both on the same axes. (It is not necessary to copy the original f and g.) (6 marks)

3.Find the sum and difference functions f + g and f g for the functions given. (6 marks)

a.f(x) = 2x + 6 and g(x) = 2x - 6

b.f(x) = x2 - x and g(x) = -3x + 1

c.f(x) = 3x3 - 4 and g(x) = -x2 + 3

4.State the domain and range for the sum and difference functions in #3. (6 marks)

5.Find the product and the quotient functions for the functions given: (6 marks)

a.f(x) = 2x + 6 and g(x) = x + 3

b.f(x) = x2 + 3x - 4 and g(x) = x - 1

c.f(x) = and g(x)=

6.State the domain and range for each resulting function in #5. (6 marks)

7.Find h(t) + k(t) if h(t) = {(-4,5), (-2,-3), (0,5), (1,3), (3,-1), (5,5)} and k(t) = {(-3,-2), (-2,6), (-1,0), (1,0), (2,-6), (3,5), (4,0), (6,-2)}. (2 marks)

8.Sagan lives in a small town which only has a weekly newspaper covering items of local interest. She delivers these newspapers to subscribers. She earns $20 per week plus an amount that depends on the number of subscribers, n, according to the function P(n) = 20 + 0.10n. An advertiser wishes to reach the homes of the subscribers of the newspaper and has offered to pay Sagan according to the function Q(n) = 30 + 0.05n.

a.Explain what the two constants in the function Q(n) represent. (2 marks)

b.What function T(n) would represent her total weekly income? (2 marks)

c.For how many subscribers would Sagan be paid equal amounts by the newspaper publisher and the advertiser? (2 marks)

9.State and explain each of the different types of symmetry studied in this unit. Give an example of each. (3 marks)

10.Can a relation that is not a function have symmetry? Explain and illustrate your answer with an example. (2 marks)

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