FALL 013 COLLEGE ALGEBRA REVIEW FOR TEST 1 Find the distance in the -plane between the two points. Give an eact answer, then give an approimation rounded to two decimal places. 1) (-, ) and (, -) Find the midpoint of the line segment joining the two points. ) (7, ) and (-8, ) Find the domain and range of the relation and determine whether it is a function. 3) {(,-), (,-7), (-6,1), (-6,-6)} Make a scatterplot of the given data. ) {(0, 3), (-3, ), (, 1), (-, ), (-1, 9)} 1) Find f(k - 1) when f() = - 3 +. Specif the domain of the function. 16) f() = - 17) f() = 9-7 Use the graph to find the domain and the range for the function. 18) Find the center and radius of the circle. ) + = 7 6) ( - 7) + ( + 6) = Find the standard equation of the circle that satisfies the conditions. 7) Center (-1, -), radius 19 8) Endpoints of a diameter (7, ) and (3, -) 19) Provide the requested response. 9) If f(-8) = -9 identif a point on the graph of f. ) If the point (7,.7) lies on the graph of f, then f( ) =. Graph f b hand b plotting points to determine the shape of the graph. Label at least 3 points. 11) f() = + 3 0) Graph f b hand b first plotting points to determine the shape of the graph. Plot and label at least 3 points. 1) f() = - Evaluate the function as indicated. 13) Find f(-16) when f() = 1 + 9. 1) Find f( 9) when f() = + 1.
Fall 013 Math 131 Review for Test 1, Page State whether the given function is linear and constant, linear but not constant, or nonlinear. 1) f() = -6 + 3 ) f() = 6 3) f() = -63-9 + 1 ) f() = + 7 Determine if the data in the table are linear or nonlinear. ) 0 6 9 1 11 1 1 3 31 6) 6 7 8 18 7 38 1 66 Epress the following in interval notation. 7) { < -6 or } 8) { 3 < } 9) { < 7} Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 33) 3 1 - -3-1 1 3-1 -3 - Identif where f is increasing and where f is decreasing. 3) f() = - 3 3) f() = - Compute the average rate of change of f from 1 to. Round our answer to two decimal places. 36) f() = + 1, 1 = 1 and = 3 30) 31) -7-6 - - -3-1 0 1 3-3 -1 0 1 3 6 7 8 9 Solve the problem. 37) The distance D in feet that an object has fallen after t seconds is given b D(t) = 16t. (i) Evaluate D() and D(3). (ii) Calculate the average rate of change of D from to 3. Interpret the result and include appropriate units of measure. 3) -7-6 - - -3-1 0 1 3 Use the graph and formula for f() to find the average rates of change of f from - to -1 and from 1 to. 38) f() = 0. - 3 3 1 - - -3-1 1 3-1 -3 -
Fall 013 Math 131 Review for Test 1, Page 3 The table lists remaining life epectanc, E, in ears for females of age. Find the average rate of change of remaining life epectanc from age 0 to age 0 and interpret the result. 39) (r) 0 0 60 70 E (r) 1.9 3.3 3. 16.0 Complete the following for the given f(). (i) Find f( + h). (ii) Find the difference quotient of f and simplif. 0) f() = 3-8 1) f() = + - 9 Find a point-slope form for the equation of the line satisfing the conditions. ) a) Slope -, passing through (6, 3) b) Passing through (-8, -) and (3, ) Write an equation in slope-intercept form for the line shown. 3) 6 7) Through (-8, ), perpendicular to = - 9-1 8) Through (, ), perpendicular to = 6 9) Vertical, passing through (9, -3) 0) Horizontal, passing through (-8, 9) Determine the - and -intercepts on the graph of the equation. 1) a) - 6 = b) = - 3 c) = 7( + ) + 1 The table lists data that are eactl linear. (i) Find the slope-intercept form of the line that passes through these data points. (ii) Predict when = -1 and =. ) - 0 f() 1-8 -18 Identif the equation as either linear or nonlinear b tring to write it in the form a + b = 0. 3) a) 7 + 7 = 0.8 b) 7-.8 = - 6 c) 7 + 19 = ( - 7) - -6-6 - -6 Solve the equation smbolicall. ) 8 + = 1 ) 3t + 6 = 7t + 1 Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. ) (, ); slope: - Write the slope-intercept form of the equation for the line passing through the given pair of points. ) a) (-8, 7) and (0, ) b) (, -6) and (, -8) c) (, -6) and (, -8) Find an equation of the line satisfing the following conditions. If possible, write the equation in slope-intercept form. 6) Through (, -6), parallel to + 3 = - 6) 8 - (6-1) = 7) 6(3-1) = 8) 1 p - 3 8 p = 9) + 60) 3-9 = + 6 + 6-8 = - 1
Fall 013 Math 131 Review for Test 1, Page Classif the equation as a contradiction, an identit, or a conditional equation. 61) a) 18m + = (m + 18) b) (f - 9) = 16f - 36 c) -1s - 3 + (3s + 8) = 0 Solve the problem. 6) Let 1 equal the left side and let equal the right side of the given equation. Graph 1 and and use the graph to solve the equation + = -. 69) A water tank can be filled in 6 minutes and emptied in minutes. If the drain is accidentall left open when the tank is being filled, how long does it take to fill the tank? 70) A rectangular Persian carpet has a perimeter of 00 inches. The length of the carpet is 8 in. more than the width. What are the dimensions of the carpet? 63) To convert a temperature from degrees Celsius to degrees Fahrenheit, ou multipl the temperature in degrees Celsius b 1.8 and then add 3 to the result. Find F as a linear function of c, and use this function to convert 6 C to F. 6) In a certain cit, the cost of a tai ride is computed as follows: There is a fied charge of $.0 as soon as ou get in the tai, to which a charge of $1.60 per mile is added. Find an equation that can be used to determine the cost, C(), of an -mile tai ride. 6) Brand A soup contains 87 milligrams of sodium. Find a linear function f that computes the number of milligrams of sodium in cans of Brand A soup. 66) A store is discounting all regularl priced items b %. (i) Find a function f that computes the sale price of an item having a regular price of. (ii) If an item normall costs $19.6, what is its sale price? Solve the problem. Round our answer to the nearest whole number. 67) A tree casts a shadow 1 m long. At the same time, the shadow cast b a 3-cm tall statue is 7 cm long. Find the height of the tree. Solve the problem. 68) Martha can rake the leaves in her ard in hours. Her brother can do the job in 6 hours. How long will it take them to do the job working together?
Answer Ke Testname: CAREVIEW1_F13 1) eact: 8 appro: 9. ) - 1, 1 3) D = {-6,, }; R = {1, -7, -, -6}, not a function ) - - ) Center: (0, 0), radius: 3 3 6) Center: (7, -6), radius = 7) ( + 1) + ( + ) = 19 8) - + + 1 = 13 9) (-8, -9) ) f(7) =.7 11) 1) (-, ) - (-3, 0) - 8 6 (0, 3) (3, 1) (, 0) -8-6 - 6 8 - -6-8 (6, ) 13) 31 1) 19 1) k - 11k + 1 16) 17) All real numbers 18) D: All real numbers, R: 19) D:, R: 0 0) D: { -6 3}, R: { 9} 1) linear, but not constant ) linear, constant 3) nonlinear ) nonlinear ) linear 6) nonlinear 7) (-, -6) [, ) 8) (3, ) 9) [, 7) 30) (-, 1] 31) (3, 7] 3) (-, -) [-1, ) 33) increasing: [, 0] [1, ); decreasing: (-, ] [0, 1] 3) increasing: (-, ); decreasing: never 3) increasing: [0, ); decreasing (-, 0] 36) 0.6 37) (i) 6, 1 (ii) 80; the object's average speed from to 3 seconds is 80 ft/sec. 38) ; 39) -0.96. On average, the remaining life epectanc decreases each ear b.96 ears between age 0 and age 0. 0) (i) 3 + 3h - 8 (ii) 3 1) (i) + 8h + h + + h - 9 (ii) 8 + h + ) a) = -( - 6) + 3 b) = 3 ( + 8) - 11 3) = 1 - ) = - + 13 ) a) = - 8 + b) = - - c) = 7-30 7 6) = - 3-3
Answer Ke Testname: CAREVIEW1_F13 7) = 9 + 16 8) = 9) = 9 0) = 9 1) a) -intercept is - 6; -intercept is b) -intercept is 3 ; -intercept is -3 6) f() = 87 66) f() = - 0.; $16.7 67) 9 m 68) 3 hr 69) 1 min 70) Width: 36 in.; length: 6 in. c) -intercept is - 9 ; -intercept is 9 7 ) (i) f() = - + (ii) when = 1, = -3 when =, = 3 3) a) Linear b) Nonlinear c) Linear ) ) 3 8 6) 1 7) 3 8) -3 9) 1 60) 3 61) a) Conditional b) Identit c) Contradiction 6) 3 1 - - -3-1 1 3-1 -3 - - = 1 63) 78.8 F 6) C() =.0 + 1.60