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MATH116 Lecture 13: M116.F15.MT-SOL

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9 Dec 2015

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University of Waterloo

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Instructions: write your student id number and uw userid at the top of this page, answer the questions in the spaces provided. There are questions on both sides of the page. There is a blank page at the end of the exam for rough work: show all work required to obtain your answers for full credit. [3: let f (x) = and g(x) = 1 x2 . (a) find a simpli ed expression for (f g)(x). 1 2x2 ) (b) find the domain of f g. For the domain of f g we rst need x that are in the domain of g, i. e. we need x to be nonzero, and in addition, the simpli ed formula for f (g(x)) needs to be de ned. We thus need 1 2x2 > 0, or 1 > 2x2, or 1 with the earlier requirement that x (cid:54)= 0, we have the domain:

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Related Questions

1. Expressthe solution set of the inequalityx^3-x^2+x-1>0<?xml:namespace prefix = v ns ="urn:schemas-microsoft-com:vml" /> <?xml:namespace prefix = ons = "urn:schemas-microsoft-com:office:office" /> ininterval notation.

2. Find the value ofk such that the line kx-3y=10 is perpendicular to the line2x+3y=6.

3. Find the point(s)of intersection of the graphs of y=x-1 and2x^2+3y^2=11.

4) For f(x)=2x^2-4x+1, find and simplifyf(a+h)-f(a)/h

5) For f(x)=x^2+x and g(x)=-4x+3 , find andsimplify:

a) (f*g)(x)

b)(g*f)(x)

c)(g*g)(x)

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1. Factor out the GCF from thepolynomial.
20m^9 + 6m^7 + 20m^5

2(10m^9 + 3m^7 +10m^5)
No common factor
m^5 (20m^4 + 6m^2 +20)
2m^5 (10m^4 + 3m^2 +10)

2. Find the solution to the system by addition(elimination) method.
4x + 15y = 15
8x - 3y = -3

(1, 0)
(0, 0)
(0, 1)
(1, 1)

3. (11p + 4)(11p - 4)

p^2 - 16
121p^2 + 88p - 16
121p^2 - 16
121p^2 - 88p -16

4. Find the solution to the system by addition(elimination) method.
2x + 15y = -91
9x + 5y = 28

(-5, 7)
(7, -7)
(9, -9)
(-7, 7)

5. Factor by grouping.
18x^3 + 15x^2 + 12x + 10

(3x^2 + 2)(6x + 5)
(18x^2 - 2)(x - 5)
(3x^2 - 2)(6x - 5)
x(18x + 2)(x +5)

6. (x + 3y)(x + 5y)

x^2 + 5xy + 15y^2
x^2 + 8xy + 8y^2
x^2 + 8xy + 15y^2
x + 8xy + 15y

7. 6x^7 (9x^7 + 12x^2 - 7)

54x^7 + 72x^2 - 42
54x^14 + 72x^9
54x^14 + 72x^9 -42x^7
54x^14 + 12x^2 -7

8. 15x^2 - 12x + 10x - 8

(15x + 2)(x - 4)
(15x - 2)(x + 4)
(3x - 2)(5x + 4)
(3x + 2)(5x -4)

9. For the polynomial, state the degree andwhether or not the polynomial is a monomial, a binomial, or atrinomial.
5x^3y^4 - 8x^5y^6 + 8

Binomial, degree 7
Trinomial, degree 3
Trinomial, degree18
Trinomial, degree11

10. (3x^8 + 2x^7 - 4x^6 + 8) + (7x^8 - 4x^7 +8x^6 + 1)

10x^8 - 2x^7 + 4x^6 +9
12x^42 + 9
10x^26 - 2x^14 + 4x^12 +9
4x^8 + 4x^7 + 4x^6 +9

11. (2n^5 - 3n^3 - 6) - (5n^5 - 14n^3 -3)

-3n^5 + 2n^3 - 9
-3n^5 + 11n^3 - 3
5n^8
-3n^5 + 11n^3 -9

12. Use the substitution method to solve thesystem.
x - 4y = -13
7x - 5y = -22

(1, 4)
(-2, 4)
(-1, 3)
No solution

13. Use the substitution method to solve thesystem.
8x - 6y = 32
2x - 2y = 8

(3, 1)
(4, 1)
(4, 0)
No solution

14. Terms in a polynomial are separated byaddition or subtraction.

15. A polynomial is an algebraic expression ofone or more terms.

16. A solution of two linear equations in twovariables is an ordered pair that is a solution to eachequation.

17. The greatest common factor will always begreater than the largest factor of each term of theexpression.

18. A system of equations in two variables mayhave infinite solutions.

19. When two or more algebraic expressions aremultiplied, each expression is called a term.

20. Factoring is multiplication inreverse.