Algebra Questions

Use the properties of logarithms to expand the following logarithmic expression as much as possible Where possible evaluate logarithmic expressions log 10 9 log14 10 9

Find a polynomial of least possible degree having the graph shown 4 74 50 0 24 2 6 f x Type your answer in factored form

Equation 4 2 ex 1 x 52 2x 25 2 4 x 1 256 Answer Enter an equation in terms of x and y D

K Find a polynomial of least possible degree having the graph shown Use a leading coefficient of 1 or 1 f x Simplify your answer CITE 6 A H 5d 10 64 100

Graph the polynomial function Factor first if the expression is not in factored form f x x 8x 11x 20 Use the graphing tool to graph the function Click to enlarge graph Click the graph choose a fool in the palette and fol AY 40 32 24 16 8 8 16 24 32 E 40 A UJ

Find a polynomial of least possible degree having the graph shown Use a leading coefficient of 1 or 1 f x Simplify your answer CIB Ed 100 064

Calculate the distance between the points E 2 3 and C 6 7 in the coordinate plane Give an exact answer not a decimal approximation

Use the intermediate value theorem to show that the polynomial function has a real zero between the numbers given f x 4x 2x 6 1 and 2 What is f 1 Simplify your answer Type an integer or a fraction

Using the Intermediate Value Theorem show that the function f has a zero between a and b f x x 3x 2 9x 13 a 5 b 4 What is f 5

Find a polynomial of least possible degree having the graph shown 8 6 95 50 0 45 3 5 f x Type your answer in factored for

polynomial of least possible degree having the graph shown 0 1 U f x Type your answer in factored

1 In an arithmetic sequence the first term is 8 and the sum of the first 20 terms is 790 a Find the common difference

ex 4 A geometric Series has first term 0 and common ratio Ferm of the series is 4 and the Sum r The Second of infinity of the series is 25 al Show that 25r 25 r 4 0 two possible vales b Find the the two Find the corresponding two possible values of a of the first in terms of the d Show that the Bush T Sories given by Sn 25 1 r

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f 240 7 a The slope is Type an integer or a simplified fraction The y intercept is 0 240 Type an ordered pair Type an integer or a simplified fraction The x intercept is 7 0 Type an ordered pair Type an integer or a simplified fraction b Write an equation that defines f f x Simplify your answer Use integers or fractions for any numbers in the expression 280 240 200 169 120 80 40 240 120 160 200 240 280

2 5 Sketch two triangles ADEF AGHF If DE 72 when GH 60 and EF 54 what is the length of side of HF Remember to draw two triangles and label their vertices correctly with corresponding parts labeled

43 Express the following using exponents 1282 204

24 Analyze the following graph of a system of two equations Determine the x and y values of the solution of the system State your answers as decimals not fractions y 1

28 A eight hour work day includes a total break time of 0 8 hours What percent of the work day is used for breaks Round your answer to the nearest hundredth of a percent if necessary 29 Using a calculator 96 rounded to the nearest hundredth is x 30 Solve for t Do not use a calculator Keep radical in simplest form t 81 0 or

5 Use the following scenario and frequency table to answer the question A classroom of 15 students polled to see who had studied for a quiz that morning The results were as follows No Boys Girls Total Yes 3 4 7 CT 5 3 38 8 Total 8 7 15 Which of the following describes a joint relative frequency O Among the 7 girls 4 studied for the quiz O Of the 15 students surveyed 7 were girls Of the 15 students 5 were boys who did not study for the quiz Of the 15 students surveyed 8 people neglected to study

25 Find the distance t between a termite and a magnifying glass if you can see a termite clearly when your eye is 4 cm away from the glass and the focal length of the glass is cm Hint the formula for this 16 8 scenario is in your lesson content t x cm ENGLINE JUUNTARIL 48 126 NE PERALA RESEERIA 27339 SAUN BALEARE MEANIE LES KONDELLEERE

31 Given ATUV when ZV is the right angle and t 15 and v 18 the length of the leg u is x 32 How many values of x make 6x 36 6 x 6 a true statement O infinite values one value no values 33 Replace the with the correct symbol or which will make a true statement from the following expression

36 Use substitution to solve the system Determine how many solutions there are T 28 2 5r 5s 8 number of solutions

8 The cost of sending a package through first class mail is indicated in the table below Find the domain of this function relating weight of the package to mailing cost Weight ounces Cost 0 45 0 65 0 85 1 05 less than 1 between 1 and 2 between 2 and 3 between 3 and 4 O Domain 0 45 weight 1 05 Domain 0 weight 4 O O Domain 3 weight 4 Domain 0 weight 1

26 Find the unknown measurement b in this parallelogram shown Height is 2 3 feet and the area is 18 square feet The formula for the area of a parallelogram is A base xx height Round to the nearest hundredth b ft 2 3 ft b length of the base

19 Two ordered pairs that are solutions of the equation 2y 6x 14 are O 7 14 1 10 O 7 14 4 19 O 7 14 1 5 O 7 28 4 19 20 Solve for y 6 3 y x

23 Observe the following graph y H L If 8 is the x intercept of line L what is the slope and y intercept of line L slope y intercept H K

f x Simplify your answer Use integers or fractions for any numbers in the expression 12 RA 12

8 Solve the linear systems of equations using the elimination or addition multiplication method Write none in both blanks if there is no solution 11x 8y 100 4x6y 26 x x y 9 Find the equation of a line passing through points 6 7 5 8 y x

7 Find y when r 22 if y varies directly as a and y 40 when 11 84 39 O 85 76 78 83 O 80

2 A garden s length 1 is five feet longer than the width w If the perimeter is 38 feet choose the best equation for the situation O4w 5 38 O w 5 w 38 O4w 10 38

Find a formula for the inverse of the following function if possible A x x 5 5

Let f x 2 x state the relation between the graphs of the function and invorse sketch the graphs of f and f on the same of axes pair PO MNI 12 8 7 6 5 3 2 10 2 3 4 5 6 7 8 9 10

Let f x 7x 2 and g x 4x 5 Find f g x f g x fg x and f g x Simplify your answer x Give the domain of each

Show that 3 5 27 is a solution of the equation x 7x 16 25 0 To show that 3 5 2i is a solution of the equation x2 7x 16 25 0 the first step is to substitute 3 5 2i for x in the equation x 7x 16 25 0 Perform the substitution 0 35 27 2 7 3 5 27 16 25 Do not evaluate What is the most useful next step OA Take the square root of both sides of the equation to clear the exponent OB Multiply both sides of the equation by the complex conjugate of the imaginary number in parentheses c Expand the right side of the equation D Divide both sides of the equation by the constant 16 25 Apply the next step 0 12 25 7i 7i 4 24 5 14 16 25 Do not combine like terms Now combine like terms 4

f x x 3 and g x 5x find the following a fog x and its domain b gof x and its domain a fog x Simplify your answer

T a f x 2x 3 x 1 Given f x a find f b describe domain and range of f c Show that f f x x and f f x x y 2x 3 x 1 x 2 2x 3 x 1 Domain off x 1 Range y 2

Use the graph to evaluate each expression a f g 2 b f g 3 c fg 1 d f g 2 6

Let f x x 1 h x x 5 Find f o h 3 foh 3

of Rudy Meangru Show that the functions f x x 3 and g x x 3 are inverses by verifying that f g x x and g f x x f g x f x 1 g f x g x 1

Use the given table to evaluate each expression in parts a through d if possible a f g 2 b f g 4 c fg 2 d 0 a f g 2 Simplify your answer X 2 0 2 4 f

a f x 2x 3 x 1 y 2x 3 x 1 3 Domain off x 1 4 Range y 2

6 Solve the following equation for x The domain of both fand its inverse is the set of all real numbers and f 5 3 7 3f 2x 1 12 f 2x 1 5 f f 2x 1 f 5 Given f 5 3

Let f x 7x 2 and g x 4x 5 Find f g x f g x fg x and f g x 11x 3 Simplify your answer f g x Simplify your answer H x x Give the domain of each

S x 2x f 2x 3 3 1 2x 3 x 1 2 2x 3 3x 3 2x 3 2x 2 x x x 2 5x 5 times the numerator and denominator by x 1

5 Letf x 2 x 3 Deseribe the domain of the and range in verse function

Let f x 7x 2 and g x 4x 5 Find f g x f g x fg x and 1 f g x Simplify your answer x Give the domain of each

4 Le f be defined as f x x 1 2x 1 Find f 3 in two different ways One Way Find f and then compute f 3 Another way Solve for x f y x 1 2x 1 X 3

5 Let f x 2 x 3 a Show that f is one to one f x x 3 f x x 3

The graph of f x is shown in red Draw the graph of g x f x Make sure to start at one of the endpoints not the middle point After finishing the graph click outside the grid to stop drawing 8 7 6 5 4 3 2 7 8 96 5 4 3 2 1 2 3 4 5 69 7 8 1 Clear All Draw Polygon 2 3 4 5 6 7 8

The graph of a linear function f is shown a Identify the slope y intercept and x intercept b Write the equation that defines f a The slope is Type an integer or a simplified fraction 10 8 230 200 160 20 80 40 240 80 120 160 200 240 280