Honors Algebra II 2 nd Semester Review Sheet ) Perform the indicated operation.!! = 3!!!!! =!!! 4) Verify that f and g are inverse functions.

Transcription

1 Name Honors Algebra II nd Semester Review Sheet Chapter ) Evaluate ) Perform the indicated operation. = = () () g() *f() ) Find the inverse. = = + ) Verify that f and g are inverse functions. 5) Solve the equations. = 6 6 = 6 = d. = 6 f( ) g 6 5 = + 5 ( ) = 6 6) The fetch f (in nautical miles) of the wind at sea is the distance over which the wind is blowing. The minimum fetch required to create a fully developed storm can be modeled by s =. f + +.where s is the speed (in knots) of the wind. Determine the minimum fetch required to create a fully developed storm if the wind speed is 5 knots. (Round to decimal places.) 7) Graph and give the domain and range. Chapter = + = 8) Tell whether the function represents eponential growth or eponential decay. f( ) = 5 f( ) =

2 f( ) = e 9) A house was purchased for $9, in 995. If the value of the home increases by 5% per year what will it be worth in? ) You buy a new car for $,. The value of the car decreases by.5% each year. Estimate when the car will have a value of $8. ) You deposit $8 in an account that pays 5.5% annual interest compounded continuously. What is the balance after 6 years? ) You deposit $ into an account that pays % annual interest compounded quarterly. How much money will you have in years? ) Simplify the epression. e e 8 y e e + ) Graph and write the equation of the asymptote, the domain, and range. f( ) = f( ) = + f( ) = e 5) Use log 5. to approimate log 5. 6) Condense the epressionlog log. 7) Epand the epression 8) Evaluate log7 5. ln y 9) Find an eponential function to the form of (,6) and (7,). ) Solve. (Check a and b for etraneous solutions.) log log = log + 6 log = log + log + 8 = d. 5 + "# = 5 y = ab whose graph passes through the points e. f. + 5 = = e.

3 ) Graph and write the equation of the asymptote, domain, and range. f( ) = + log f( ) = ln ) Graph f( ) = e. Give the domain, range, equation of the asymptote, and the y- + intercept. 5 ) The spread of a virus through a student population can be modeled by s = where.8t + 999e s is the total number of students infected after t days. Tell when the point of maimum growth in infections is reached. ) Find a power function of the y b = a whose graph passes through the points (, ) and (, ). 5) Most tornadoes last less than an hour and travel less than miles. The speed s (in miles per hour) near the center of a tornado is related to the distance d (in miles) the tornado travels by this model: s= 9log d Estimate how far a tornado traveled if the wind speed was about 8 miles per hour. 6) The moment magnitude M of an earthquake that releases energy E (in ergs) can be modeled by M =.9ln E+.7. How much energy did a 9.5 magnitude earthquake release? Chapter 5 7) The variables and y vary inversely. Write an equation relating and y, if = and Then find y when =. 8) The variable z varies jointly with and y. Write an equation relating, y, and z, if y =. =, y =, 5 z =. Then find z when = - and y =. 9) The volume of a geometric figure varies jointly with the square of the radius of the base and the height. Write an equation for the volume. Estimate the constant of variation in V = 6. in, r=. in, and h =.5 in. 6.6d ) The number f of flies eaten by a praying mantis in 8 hours can be modeled by f = where d is the density of flies available (in flies per cubic centimeter). Approimate d the +.7 density of flies when a praying mantis eats 5 flies in 8 hours. (Round to decimal places.) ) Graph and Give the domain, range, vertical asymptotes, holes, and horizontal asymptotes.

4 y = + +. y = 9 y = ) From 98 to 995, the total revenue R (in billions of dollars) from hotels and motels in the U.S can be modeled by R = where is the number of years since 98. In what year. + was the total revenue approimately $68 billion? ) Almost all of the energy generated by a long- distance runner is released in the form of heat. The rate of heat generation h g and the rate of heat released h r for a runner of height H can be modeled by hg = kh V and hr = kh where speed/ Write the ratio of heat generated to heat released. Simplify. ) Perform the indicated operation. Simplify the results ) Simplify. k and k are constants and V is the runner s ) Solve. 9 + = = =

5 Chapter 8 7) Find the distance between the two points, (- 8, ) and (, 7). Then find the midpoint of the line segment connecting the two points. 8) Use the given distance d between the two points to solve for. (, ),(, ); d = 9) A Street light can be seen on the ground within yd of its center. You are driving and are yd east and 5 yd south of the light. Write an inequality to describe the region on the ground that is lit by the light. Is the street light visible? ) An amusement park has an elliptical garden at its entrance. The garden is ft long and ft wide. Write an equation of the ellipse. What is the area of the garden if A = π ab. ) One focus of the summer solstice hyperbola is 7 inches above the ground. The verte of the aluminum branch is 66 inches above the ground. If the - ais is 55 inches above the ground and the center of the hyperbola is at the origin, write an equation for the summer solstice hyperbol ) A cellular phone transmission tower located miles west and 5 miles north of your house has a range of miles. A second tower, 5 miles east and miles south of your house, has a range of 5 miles. Write an inequality that describes each tower s range. Do the two regions covered by the towers overlap? ) Graph. ( ) ( y ) + + = 5 + 9y = 5 8y 9 = 79 ) Write the equation of the given conics. center(,) Circle: radius Verte(,5) Ellipse: Co verte(,) Center(, ) Verte(,) Hyperbola: Co Verte(,) Center(,) Verte : (,) d. Parabola: Focus : (, ) 5) Which direction does the parabola open, up, down, left, or right. = y

6 = y y= d. y = 6) Classify the conic section. d. 9 + y + 6 y+ 6= y = y y + = 6y + + 6y+ 6 = + y = 8 7) Find the point of intersection, if any of the graphs in the system. y = 8) The range of a radio station is bounded by a circle given by the following equation + y 6 =. A straight highway can be modeled by the following equation y= +. Find the length of the highway that lies within the range of the radio station. 9) Graph. f( ) = + +, f( ) =,< < 8, 5) The table shows the number c of cranes in Izumi, Japan, from 95 to 99 where t represents the number of years since 95. Use eponential regression to find an eponential model for the data and then estimate the number of cranes in the year. t c