Math 101

Find the domain of the function using interval notation: f(x)= sqrt(14−13x)

(-infinity, 14/13]

Find the domain of the function using interval notation: f(x)=3/(x-4)

(-infinity, 4) U (4, infinity)

Factor the polynomial: 2n^2 − n − 45

(2n+9)(n-5)

Add the rational expressions, then simplify: (4/(a+1))+(5/(a-3))

(9a-7)/(a+1)(a-3)

Subtract the rational expressions: ((c+4)/4)-((c-5)/5)

(c+40)/20

Factor the polynomial: m^2 − 20m + 100

(m-10)^2

Simplify the rational expression: (x^2 − 16)/(x^2 − 5x + 4)

(x+4)/(x-1)

Multiply the rational expressions and express the product in simplest form: ((x^2-x-6)/(2x^2+x-6))((2x^2+15x-27)/(x^2-9))

(x+9)/(x+3)

Simplify the given expression −7 × [25 ÷ (8 − 3)^2]^2

-7

If a point is located on the y-axis, what is the x-coordinate? x=___

0

Find the difference. (Simplify your answer completely) (19x^2 + 5x) − (6x^2 − 13)

13x^2+5x+13

Find the difference:(15b^4 − 3b^3 + 16b^2 − 18b + 7) − (4b^3 + 8b^2 + 4b)

15b^4-7b^3+8b^2-22b+7

Given the function f, find f(−3), f(2), f(−a), −f(a), and f(a + h): f(x)=(8x-5)/(3x+4) f(-3)= f(2)= f(-a)= -f(a)= f(a+h)=

29/5, 11/10, (-8a-5)/(-3a+4), -((8a-5)/(3a+4)), (8a+8h-5)/(3a+3h+4)

Simplify the expression: 7 × 5 + 16x ÷ 8 − 35

2x

Find the product: (5d − 2)(7d + 9)

35d^2+31d-18

Find the greatest common factor: 21x + 9xy − 12xy^2

3x

Expand the binomial: (7m − 3)^2

49m^2-42m+9

Simplify the expression: (8/6t−3)3

4t-9

Multiply the binomials: (9c + 1)(9c − 1)

81c^2-1

What is the difference between a relation and a function?

A relation is a set of ordered pairs; a function is a special kind of relation in which no two ordered pairs have the same first coordinate.

What is the order of operations?

A set of rules that define the order in which the different operations should be performed so that expressions can be evaluated consistently.

What is the difference between the input and the output of a function?

The input is the independent variable; the output is the dependent variable because it depends on the value of the input.

Determine whether the relation represents a function: {(a, b), (c, d), (a, c)}

The relation is not a function because the input a corresponds to two different outputs.

Why does the vertical line test tell us whether the graph of a relation represents a function?

When a vertical line intersects the graph of a relation more than once, it indicates that for that input there is more than one output, which means the relation is not a function.

Find f(a+1): f(x) = x^2 + 1 f(a+1)=

a^2+2a+2

Many times, multiplying two binomials with two variables results in a trinomial. This is not the case when the product is a difference of two squares. Explain why the product is a binomial in this case. Multiplying two binomials yields the difference of two squares, if the product of the outside terms and the product of the inside terms are __________ of each other. When these terms are added, their sum is __________ term, #

additive inverses, 0

Find the x-intercept and the y-intercept without graphing. Write the coordinates of each intercept: 4x − 9y = 36 x-intercept: y-intercept:

x-intercept: (9,0) y-intercept: (0,-4)

Find f(x) − g(x) = (f − g)(x). Simplify: f(x) = 5x^2 − 3x + 5 g(x) = 13 − x^3 − 2x^2

x^3+7x^2-3x-8

Multiply the polynomials: (x − 2)(x^2 − 4x + 2)

x^3-6x^2+10x-4