Algebra Questions

27 4 6n 4 n 1 11 2 1 0 1 2 5 6 7 8 28 16 8x 7x 2 8x 4 3 2 1 0 1 2 3

21 13 1 2x 10 8 6 22 9 8 x 153 2 5 6 7 10 11 12

14 98x 32x 0

Simplify the following expressions x 1 1 x

8 x 9x 4

6 9x 5x 9 6x 7x 5x 9

18 If a is one of the solutions of the equation x x 20x 0 and a 0 what is the value of a A 0 B 1 C 4 D 5

7 3x 2 2x 5 x 8

2 12x 8x 3x

17 x x 56

16 x 27 0

1 f x 14

10 Find the zeros y x x 2 x 5

15 4x4 1 0

11 Write the polynomial in factored form and standard form with zeros 4 2 7

13 3x 24 0

4x 6x 9 9 9x 8x 7x 3

2 f x 19 13x 6x 2x

9 5x 6 x 4x 3

5 11x 6x 8 15x4 3x 5x 7x 10

6 9x 5x 9 6x 7x 5x 9

3 f x 8x 9x 7

rite 5x 25 as an equivalent expression with a denominator of x 5 x 1

Determine which of the following graphs is the graph of the given function 3x 6 f x z x 2 A C 18 A B D k 7 A U

Simplify the expression Then write the expression as an equivalent expression with a denominator of x

Find the LCD for each set of rational expressions x 6 and 8x 24 14x 10x 30

Find the rational function s asymptotes x intercepts and holes Also sketch the graph of the rational function Then list the domain and range using interval notation x 4 X 4 f x 9 T

Find the LCD for each set of rational expressions 12x 15x 60 and 5 x 9x 20

e the rational functions below to answer the following questions f x 2x 4x x 4 State the point of discontinuity i e hole of the function x Identify the x intercept of the function Find the vertical asymptotes if any of the function

Select which statement of the following rational functions given is true f x 3x 6 x 3 A The graph has no asymptotes B The graph has a vertical asymptote at x 2 C The graph has a horizontal asymptote at y 3

Use the rational functions below to answer the following questions f x 3x 12x x2 5x 4 State the point of discontinuity i e hole of the function x Identify the x intercept of the function Find the vertical asymptotes if any of the function

Find the rational function s asymptotic x intercepts and holes Also sketch the graph of the rational function Then list the domain and range using interval notation f x x 2 x 2x 3 19 7 ge 7 0

Find the rational function s asymptotes x intercepts and holes Also sketch the graph of the rational function Then list the domain and range using interval notation f x x 1 x 3x 4 on sa 7 7 7 0 5

To test if the graph lies above or below the x axis create a number line with intervals Then choose test values before in between and after the intervals to determine if the function is positive or negative in that area A positive value means the graph is above the axis and a negative value means the graph is below the axis Try This Practice testing values to determine if the values are above or below the axis Circle if the graph of f x would be positive or negative in areas A B C and D Area D is done for you below A B C f x x 2 x 1 x 3 x axis Area A Area B Area C Area D 2 x 10 f 10 Match the appropriate test values for each area x 10 x 1 5 x 5 x 0 12 11 7 1 12 77 3 D x 2 Sign of f x x 1 x 3 positive

Graham wants to take snowboarding lessons at a nearby ski resort that charges 40 per week The resort also charges a one time equipment rental fee of 99 for uninterrupted enrollment in classes The resort requires that learners pay for three weeks of classes at a time The function f x represents the situation f x 40x 99 A There is a zero at 0 B There is an asymptote at y 40 DC There is an asymptote at x 0 D There is a vertical shift up 99 units X Select two choices that are true about the function f x

Rewrite the function in the form g x a using inequalities 4x 15 2x 6 a 1 k and graph it Also state the domain and range 5 3 5 4 2 3 3 2 1 2 1 0 1 N 3 4 5

Which function is graphed to the right 1 A f x 3 x 2 B f x 1 2 x 2 3 c f x 2 1 x 3 5 4 3 N 2 5 1 0 F 2 4

Ex 6 3 x 1 7

Ex2 x 50

Ex 6 3 x 1 7

Ex 1 x 81

cs but no term term from ax2 bx c 1

Ex 4 1 3 7

Ex 5 2 x 4 32

Ex 3 3x 6 60

Rewrite the function in the form g x a 1 k Also state the domain and range using inequalities x h g x 4x 11 x 1

Amy has purchased a basic letterpress kit for 140 She plans to make wedding invitations She estimates hat the cost of the paper and envelope for each invitation is 2 Model this situation with a rational Function that gives the average cost of a wedding invitation when the cost of the kit is included in the calculation Use the graph of the function to determine the minimum number of invitations that brings the average cost below 5 2w 140 W Given C w represents the average cost in dollars of a wedding invitation when the cost of the kit is included graph it using key features Then select two choices that are true about the function C w A There is a zero at 2 B There is an asymptote at x 0 C There is an asymptote at y 2 D There is a y intercept at 2 Average cost dollars 5432768 0 C W 20 40 60 80 Number of invitations A zero implies an x intercept

Rewrite the function in the form g x ah k Also state the domain and range using inequalities 1 g x 4x 11 x 1

Identify the transformations of the graph of f x 1 x that produce the graph of the given function g x Then graph g x on the same coordinate plane as the graph of f x by applying the transformations on the asymptotic x 0 and y 0 to the reference points 1 1 and 1 1 Also state the domain and range of g x using inequalities g x 2 1 6 6 4 3 2 1 0 1 12 5

Rewrite the function in the form g x a inequalities g x 3x 8 x 2 k and graph it Also state the domain and range using 6 4 2 6 2 2 y 2 4 6 x