Algebra Questions

0 Solve the following equation for x x 4x 5 2x 10 2 A x 5 7 B x 7 x 5 D x 3 5 7

7 Write the expression below in simplest form x8 24 A B D a V7

6 Kristen is solving a radical equation and determines that the equation has no solution Which equation is Kristen attempting to solve 0 6 2

3 What is the solution set for the equation 56 x x A 7 8 B 7 C 8 7 D 7 7

If Cierra invests 5 000 into a fund that earns 6 5 interest compounded annually how long will it take for her investment to grow into 200 000 Use A p 1 r O About 59 years O About 28 years

The population of owls in an area was estimated to be 200 with a decline rate of 2 each year Which of the following functions model the estimated population of owls in t years Use A p 1 r t OP t 200 0 98 OP t 2 200

Solve for x Be sure to check for possible extraneous solutions and round to the nearest thousandth In x 6 ln 5 2 Ox 22 945 Ox 43 968 Ox 42 945 Ox 32 625

In chemistry logarithms are key to calculating the pH of a solution pH log H In this equation H is the hydrogen ion concentration Fin the hydrogen ion concentration of a substance with a pH of 5 O 10 5 510

Expand the logarithm log2 m5n JA O log2 5m log2 3n log2 4p 5 log2 m 3 log2 n 4 log2 p

Solve Be sure to check for any extraneous solutions 2 ln a ln 4 In 16 Ox 8 Ox 8

Solve the logarithmic equation using properties 2 ln 3 ln x 4 no solution X 13

Solve the logarithmic equation using properties loga x 10 3 Ox 54 O x 71

11 log 16z x 27 6

5 3 6 2

8 1 8 13 2 O Yes O No O O Yes 2 a Does this table represent a function of x 9 No 3 12 b Does this table represent a one to one function of x 9 c If you answered No in the previous question remove one entry from the table form of an ordered pair so that the new table defines a one to one function Write answer in the form x y in the box below If you answered Yes in the previous question enter NA in the box below

Use the given graph of the function y f x to find the indicated values Click on the graph to see the coordinates of its points a f 4 b f 3 c f 0 d 1 5 0 5 1 1 W

same road each traveling at a constant rate The distance between two cars can be modeled by the function d m 5280m where d is the distance between the cars in feet m minutes after they left the gas station a Express the number of minutes since the cars left the gas station as a function of the distance between the two cars m d m d b Evaluate m 105600 m 105 600 c Select the statement that best describes the values from b When the two cars are m 105600 miles apart they have been traveling for 105 600 hours O When the two cars are 105 600 feet apart they have been traveling for m 105600 minutes When the two cars are m 105600 feet apart they have been traveling for 105 600 minutes

The function below is one to one Find the inverse function f y 4 x 6 f x 1

The cost in to make a cupcakes is given by the function of x below c x 3 6x 5 a Express the number of cupcakes that can be made as a function of cost x c b Find the value of x 80 Round to two decimal places if necessary c Interpret the meaning of x 80 O The profit from making and selling 80 cupcakes The number of cupcakes that can be made with 80 O The cost to make 80 cupcakes The profit from making and selling 80 cupcakes

Let f x 10x 5 and g x a Calculate and simplify f g x f g x b Calculate and simplify g f x g f x x 3 25 O No c Are f x and g x inverses of each other O Yes

Suppose y is a function of a that does the following steps in order The input is multiplied by 7 Then add 5 Then divide by 8 a Find the rule of the function y b Describe what the inverse function does to its input in order The input is divided by 8 then add 5 then multiply by 7 O The input is divided by 8 then add 5 then multiply by 7 O The input is divided by 7 then subtract 5 then multiply by 8 O The input is multiplied by 8 then subtract 5 then divide by 7 c Give the inverse function as a function of y

Given the function of x below find the inverse function x y x 3 x 1 x y y x

During a road trip the function f t gives the total number of miles driven after t minutes Find f 80 and f 70 using the table below t minutes 30 50 80 70 80 100 120 70 f t miles 70 80 100 120 140 150 Choose all correct statements below f inputs the time spent traveling and outputs the distance traveled Of inputs the distance traveled and outputs the time spent traveling

Fill in each blank so that the resulting statement is true In the following long division problem the first two steps have been completed 2x 3x 6 6x 9x 5 6x 12x 2 The next step is to subtract 2 from which obtains Then bring down and form the new divide

Use the parent function f x b and transformation techniques to graph g x 42 5 2 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of g Select all transformations that apply Horizontally stretch the graph of f by a factor of 2 Reflect the graph of f about the y axis Shift the graph of f 5 units to the left Horizontally compress the graph of f by a factor of 5 Shift the graph of f 5 units to the right Shift the graph of f 2 units up Shift the graph of f 2 units down Vertically compress the graph of f by a factor of 5 Vertically stretch the graph of f by a factor of 2 Reflect the graph of f about the z axis

Find a formula for the inverse of the following function if possible F x 2 x 2

Write an equation for the polynomial graphed below 5 4 3 2 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 Q

Find the exact value of the following logarithmic expression In 1 2 e2 11 1 In

Write the following exponential equation in its equivalent logarithmic form 12 144 The equation in logarithmic form is

7 Dawn Keith and John are all working on a history project Dawn spent 1 2 hours less than 5 times as many hours on the project as John did Keith spent 1 2 hours more than 4 times as many hours on the project as John did If Dawn and Keith spent the same amount of time working on the project how many hours did John spend working on the project

Use the parent function f x 6 and transformation techniques to graph h z 2 3 Also indicate which transformation s is are applied Determine the domain range and horizontal asymptote of h Select all transformations that apply Shift the graph of f 3 units to the left Reflect the graph of f about the c axis Horizontally compress the graph of f by a factor of 3 Shift the graph of f 3 units to the right O Horizontally stretch the graph of f by a factor of 3 Reflect the graph of f about the y axis Vertically compress the graph of f by a factor of 3 Vertically stretch the graph of f by a factor of 3 Shift the graph of f 3 units up Shift the graph of f 3 units down Use the parent function f x b to graph h A

Write the polynomial as the product of linear factors h x x 9x 28x 30 h x List all the zeros of the function Enter your answers as a comma separated list Enter all answers using the appropriate multip

Solve the following exponential equation 2 n TL 128

Solve the following exponential equation 3 27

Find the exact value of the following logarithmic expression log12 V12

Find the exact value of the following logarithmic expression 10 1 In In

Find the exact value of the following logarithmic expression e2 In e2

4 Complete the following graph of f given that f is an odd function 10 5 15 10 5 re 5 5 10

Find the exact value of the following logarithmic expression In e8

1 Show algebraically that the function f x x 9 is an even function Sketch the graph of f 10 9 8 7 6 5

A Coca cola 5 cents A car 500 bucks These prices may seem cheap but they were not back in the day This is due to inflation In a growing economy most goods and services increase in price over time to the tune of 2 3 each year The key is that workers wages also increase Thus a car may have only cost 500 at some point in the past but the average worker s salary was much much lower back then The inflation formula can be used to predict the future price of a good or service The inflation formula is given by FV PV 1 r t where FV is the future value of the good or service PV is the present value of the good or service r is the inflation rate and t is number of years desired Suppose the average loaf of bread costs 3 94 today and grocery inflation averages 1 75 per year Use the inflation formula to predict what an average loaf of bread will cost 36 years from now Round the solution to the nearest cent Suppose the average gallon of milk costs 3 54 today and milk inflation averages 2 10 per year Use the inflation formula to predict what an average gallon of milk will cost 15 years from now Round the solution to the nearest cent

2 Complete the following graph of f given that f is an even function 10 5 161 10 5 5 5 10

ne whether fis even odd or nether X 1 1 2

3 Show algebraically that the function f x x 4 x is an odd function Sketch the graph of f T 7 0

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 The slope is Type an integer or a simplified fraction 1088 2 Ay X

Fill in the blanks with the appropriate responses The line x 2 0 has x intercept has y intercept It The line x 2 0 has x intercept has y intercept It Type ordered pairs does not or does Undefined or 0 Does not or does Undefined or 0 have a y intercept The slope of this line is have an x intercept The slope of this line is have a y intercept The slope of this line is It have an x intercept The slope of this line is The line 4y 2 The line 4y 2

Graph the following linear function Give the domain and range Identify whether it is a constant function f x 8 Use the graphing tool to graph the linear equation What is the domain of the function Select the correct choice below and fill in the answer box to complete your choice OA The domain is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed OB The domain in interval notation is Type your answer in interval notation 3 PIRT de 16 d

md and interpret the average rate of change illustrated in the lowing graph Value of Machine in thousands of dollars 15 124 Year Q Find the average rate of change Select the correct choice below and fill in the answer box to complete your choice Type a whole number OA The average rate of change is OB The average rate of change is per year per year

Graph the line 4x 3y 12 Give the domain and range Use the graphing tool to graph the equation What is the domain Select the comect choice below and if necessary fill in the answer box to complete your choice OA The domain in interval notation is Type your answer in interval notation OB The domain is a value or list of distinct values Type an integer or a simplified fraction Use a comma to separate answers as needed

The city of Sebastian has a current population of 25 479 With a projected growth rate of 1 the population of Sebastian can be modeled by P t 25479e0 01t where P is the population t years from now Use the population growth function to answer the following questions Round solutions the the nearest whole number What is the predicted population of Sebastian 1 years from now Population What is the predicted population of Sebastian 7 years from now Population What is the predicted population of Sebastian 19 years from now Population