Algebra Questions

The sales at your high school basketball game vary directly with the number of attending If the sales for a game are 3200 when 800 people attend determine how many people attend if the sales for a game are 2200 What does the constant of variation represent in this problem The demand of Starbuck s coffee is inversely related to the price Which means as the price of the coffee goes the demand will go Sketch a graph to represent this relationship and properly label the x and y axis

Use the piecewise graph to identify the following 10 B 10 8 6 4 8 10 16 DOMAIN 18 INTERVALS OF INCREASE 20 IDENTIFY THE FUNCTION FOR THIS GRAPH 17 BANGE 19 INTERVALS OF DEC 21 EVALUATE f 4 f 0 f 6

7 In economics revenue R is defined as the amount of money received from the sale of a product and is equal to the unit selling price p of the product times the number x of units actually sold That is R xp The Law of Demand states that p and x are related As one increases the other decreases Suppose that p and x are related by the following demand equation A Express the revenue R as a function of p x 4p 100 0 p 25 B What is the revenue if 18 units are sold c Sketch the graph of the revenue function D What quantity x maximizes revenue what is the maximum revenue 700 600 500 400 Revenue dollars 300 200 100 4 8 Price dollars 12 16 20 24

2 2 3k 3k A 9k4 C 4k B 4k7 D 9k

Simplify 5 2b ba 2a b4 A 4b4a8 C 4a6b6 B 16ba D 4b6a6

Simplify Your answer should contain only positive expor 3 24 29 44 2 A 28 A C 1 1 28 D 25 B C

Integer Exponents Simplify 1 3p 3p 2p A 6p C 6p B 4p5 D 18p8 L

PopQuiz On Halloween CC GG and JJ collected 75 candies CC got five more candies than GG and GG got 10 less candies than JJ How many cadies did each one get

8 105 4 10

x 1 x 2

Give the rule of the function shown below that has the form f x log x Y 5 A 3 2 1 2 3 Shift Scroll to zoom Shift Drag to pan 6 8 S 10 X 8

a Graph the function by dragging each of the following to a correct position the vertical asymptote a first point a second point 15 f x log x 3 2 10 5 15 10 0 0 5 0 5 1 1 1 1 A 5 LO 10 I C 15

Convert each logarithmic equation into its equivalent exponential form You do not need to find the value of any variables a log3 243 5 Exponential equation b log5 25 2 Exponential equation c log4 a 2 Exponential equation d log 11 y Exponential equation

Ogarithmic function 3 S 10 Shift Scroll to zoom Shift Drag to pan 8 10 11 12 X

Give the rule of the function shown below which is a vertical shift of a basic logarithmic function 2 1 2 3 4 5 Y 2 6 Shift Scroll to zoom Shift Drag to pan t er 30 6 X 8

Identify the missing number by using logarithms and a calculator Round answers to 3 decimal places a 8 29 b 10 28 c e 45 d 6 1

Identify the missing number without using a calculator If no number makes the statement true enter DNE a log4 64 b logs 64 c log3 81 d In es e log 100000000

For each function below find the indicated inverse function Be mindful of the following when using Derivita To enter a log of any base type log b base argument log argument defaults to the base 10 In argument is the natural log which has base e a f x 7 b g x c h x 10 h y d m x e m y

Let g x 2 The following graph shows g x for a between Y a Find g 9 b Find g a 2 5 N 1 5 0 5 1 3 1 2 1 1 9 9 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 1 X

Identify the missing number without using a calculator If no number makes the statement true enter DNE a In 1 e b logo 36 c log3 81 d log 1 e logg 9

Let f x 5 The following table shows f x for various values of x f x 0 1 1 5 2 25 3 125 4 5 a Evaluate f 25 f 25 b Evaluate f 125 f 125 625 3125

Consider the logarithmic expression below and answer the following loga 64 What is this expression equivalent to O The result of 4 divided by 64 O The exponent needed on the base 4 to produce the result 64 O The fourth root of 64 The result of 64 divided by 4 Evaluate the logarithm Explain O 16 because 4 64 1 6 O 16 because 64 4 16 O3 because 4 64 O 2 2 because 64 2 2

Identify the missing number without using a calculator If no number makes the statement true enter DNE a 2 8 b 6 36 c 2 16 d e e5 e 10 1000000

Determine the value of y for each of the following Recall that the base and argument of a logarithm must both be positive a log 25 2 b logs y 1 y c log4 64 y

2 2 sin 2 z 7 b Consider the function y 2 sin What is the amplitude What is the period What is the horizontal shift Sketch a graph of the function on the axes below

Find the exact acute angle 0 for the given function value tan 0 1

Khan Academy What is the range of f A 7 6 5 4 3 2 Choose 1 answer Y 7 6 5 4 3 2 1 2 do 3 40 7 5 6 7 1 2 3 4 5 6 7 The f x values 6 0 2 4 and 7 4 f x 5 6 f x 7 The f x values 4 3 1 and 5 C

Carmen s fixed expenses are the following Los gastos fijos de Carmen son los siguientes rent cable TV Health club loan car loan car insurance 700 45 25 100 129 100 When rounding to the nearest 10 her fixed expenses are Al redondear a los 10 m s cercanos sus gastos fijos son

9 The quadratic function has a domain of 0 00 and a range of 0 0 10 The absolute value function only has an interval of increase 11 The linear equation function has a local minimum 12 The following ordered pairs represents a function 2 3 1 5 1 7 0 9 1 11 13 The end behavior of the quadratic function is as x 00 f x 0 and as x o f x 14 The end behavior of the linear function is as x f x and as x f x B 15 The x intercept for the linear absolute value and quadratic function is 0 Mentify if the following statements are True or False

um revenue B Complete the following tables for Celsius and Fahrenheit c What can you conclude about the relationship between Fahrenheit and Celsius 32 You travel often therefore you need to be able to convert Celsius to Fahrenheit so you know what types of clothes to pack for each trip A Given the following equation that represents Celsius in terms of Fahrenheit find the equation for Fahrenheit in terms Celsius C F 32 F 50 68 8 86 Price doll 16 12 0 10 20 24 30

A tb C 1 am

If UV 2x VW x 1 and UW 7 what is UV

APPLICATIONS Functions and YOSI Your monthly cell phone plan is 49 99 It includes 500 anytime minutes and charges 0 45 per minute for additional minutes The following function is used to compute your monthly cost in terms of minutes used can 49 99 if 0 x 500 L 45x 175 01 if x 500 Compute the cost of your cell phone for the following months Minutes Cost January 400 C x February 525 March rapns 600

10 The graph of a piecewise function g is shown in the xy plane for 7 x 6 Write the equation for g 74 6 5 4 3 2 1 6 5 4 3 2 1 0 1 2 3 4 5 67 2 3 4 5 6 7 tx

Use the following functions to perform the indicated operation f x 3x 9 22 m h x g x x 12 24 fog x and sate whether f and g are inverses c x x 3 h x x 5 23 2 x Restriction 25 m c 2 m x x 2x 7

You go to We Love Math Ice Cream Shop where they identify their cone selections by volume The sign in the store states that the volume V of their circular cones are V h It also states that all of the cone heights are 4 times the radius A Express the volume V as a function r B Evaluate the volume of the large cone with a diameter of 3 inches

27 Suppose that the revenue R in dollars from selling x cell phones in hundreds is R x 1 2x 220x The cost C in dollars of selling x cell phones is C x 0 05x 2x 65x 500 a Find the profit function P x R x C x b Find the profit if x 15 hundred cell phones are sold

28 The volume of a cylinder varies jointly as radius squared and height a If the constant of variation is n create an equation to represent this relationship b If the radius is 4 2 and the height is 12 5 find the volume of the cylinder

7 Santiago s weekly income after working h hours can be described by the function f below 13 5h 0 h 40 20 25h 270 h 40 Which of the following conclusions is correct f h A Santiago gets paid 13 50 an hour for up to 40 hours and an additional 20 25 per hour for hours beyond 40 B Santiago has to pay 270 in taxes if he works more than 40 hours in a week C Santiago gets paid 1 5 times his hourly rate for hours he works beyond 40 hours D If Santiago works 43 hours he gets paid 870 75

29 Write an equation in slope intercept form for the line containing the points 0 13 and 4 11 30 Evaluate 16 15 5 3 5 2

tch the transformations 2 3 8 4 7 5 6 with the correct equation Horizontal shift left Horizontal shift right dentify if the fallow Vertical shift up Vertical shift down Reflection across the x axis Reflection across the y axis Vertical stretch Vertical compression A y f x B y f x m C y f x m D y m f x m 1 E y f x m F y f x G y m f x 0 m 1 H y f x m

31 Simplify 5a4b 2a b 32 Simplify 5 18 6 50

26 Match each of the following functions with the the graph that best describes the situation a The temperature of a bowl of soup as a function of time b The population of Africa as a function of time c The height of a golf ball hit by a 5 iron as a function of time 1 11 III

2 Tony is selling boxes of cookies He charges 7 for the box plus 2 per cookie One filled box sells for 35 How many cookies will fit in the box 3 Tiana s pool has the shape of a rectangle with the dimensions shown If the perimeter of the pool is 2 000 feet what is the value of x X 2 X 5 X 2

9 3 4 B 10 5 6 10 ys x 5 8 zoom in 9 10 11 10 SHAD

3 3 2x 5y 10 4 4 5x 3y 9 T ZOO

mative com formatives 63580800 1 Sketch the graph of each linear inequality 1 y2x 3 A B D 2 2 5x y S s A B D 13 1

A3 4 3 3 2x 5ps 10 M 5 6 4 5x 3p 9 7

5 Algebra Prep 1032 Kuli Software lur SUM 2 Q2 Solve each system by elimination 5 6y 42 18x 4x 8 3y A 4 1 B 4 1 reserved 6 6 3y 3x 15 9 3x 2y A 7 5 B 7 8 ZOO

Solve the equation by graphing x 14x 49 0 First graph the associated parabola by plotting the vertex and four additional points two on each side of the vertex Then use the graph to give the solution s to the equation If there is more than one solution separate them with commas 30 B Ho 6 X Solution s x 0 DO No solution X 03