College Algebra ~ Review for Test Sections. -. Find a point-slope form for the equation of the line satisfing the conditions. ) a) Slope -, passing through (7, ) b) Passing through (-, -8) and (-, ) Write an equation in slope-intercept form for the line shown. ) 6 Graph the linear equation. ) = ( + ) - Identif the equation as either linear or nonlinear b tring to write it in the form a + b = 0. ) a) + 6 = b) + = + c) 7 - = 7( + ) - 7 Solve the equation smbolicall. ) - 6 = -6 - - 6 - - -6 Write the slope-intercept form of the equation for the line passing through the given pair of points. ) (-9, 6) and (-, 8) ) 9 - ( - ) = ) 9t - = 8t + ) 9 + + - = 9 6) 9 + - = ( + 9) - ) (-6, 0) and (-9, -) Determine the equation of the line described. Put the answer in the slope-intercept form. ) Through (-, ), parallel to - 7 = 6 6) Through (-8, -), perpendicular to 8 + 7 = -78 Find an equation of the line satisfing the following conditions. 7) Vertical, passing through (-7, -9) Solve. 8) Horizontal, passing through (, ) 9) The time T necessar to make an enlargement of a photo negative is directl proportional to the area A of the enlargement. If seconds are required to make a in enlargement, find the time required for a 70 in enlargement. Classif the equation as a contradiction, an identit, or a conditional equation. 7) a) k - 9 = (k - ) b) (f + ) = 0f + c) (8t + ) = 6(t - ) 8) Brand A soup contains 8 milligrams of sodium. Find a linear function f that computes the number of milligrams of sodium in cans of Brand A soup. Round our answer to the nearest whole number. 9) A tree casts a shadow m long. At the same time, the shadow cast b a 8-cm tall statue is 9 cm long. Find the height of the tree. 0) A rectangular Persian carpet has a perimeter of 7 inches. The length of the carpet is 6 in. more than the width. What are the dimensions of the carpet?
Math, Review for Test Page Use the given graphs of = a + b to solve the inequalit. Write the solution set in interval notation. ) - + Provide an appropriate response. ) The graphs of two linear functions f and g are shown in the figure. Solve (i) the equation f() = g() and (ii) the inequalit g() < f(). 9 8 7 6 (, ) (, ) - - - - 6 7 8 - Solve the inequalit smbolicall. Epress the solution set in interval notation. ) a) 7a - > 6a - b) -(a - ) -8a + 7 c) - < ) a) - < - 7 8 b) -7 8-9 6 Solve the inequalit graphicall. Epress the solution in set-builder notation. ) 6 - + Solve the equation. ) r - = 7 Solve the absolute value inequalit. Write the solution set using interval notation. ) a) 9 + < 6 b) b + - > c) + 6 ) b + - > Solve the inequalit graphicall, numericall, or smbolicall, and epress the solution in interval notation. Where appropriate, round to the nearest tenth. ) + < 6 6) b + 6-8 = 0 7) m + + = 8) t - + 9 = Solve the absolute value equation. 9) - = + 0) - 6 = - ) The inequalit T - 8 describes the range of monthl average temperatures T in degrees Fahrenheit at a Cit X. i) Interpret the inequalit. ii) Solve the inequalit. Identif f as being linear, quadratic, or neither. If f is quadratic, identif the leading coefficient a. 6) a) f() = - 7 b) g() = 8 + 7 c) h() = + d) j() = - -
Math, Review for Test Page Evaluate. 7) a) Given f() = + 6 +, find f(-). b) Given f() = - +, find f(). Use the graph of the quadratic function to determine the sign of the leading coefficient a, the verte, and the equation of the ais of smmetr. Then state the intervals where f is increasing and where f is decreasing. 8) -6 - - - - - - 6 - - - - The graph of f() = a + b + c is given in the figure. State whether a > 0 or a < 0. ) a) b) - - - - 9) - - - - -6 - - - - - - 6 - - - - Identif the interval where f is increasing or decreasing, as indicated. Epress our answer in interval notation. 0) a) f() = ( + ) + b) f() = - + 6 c) f() = -6 + - Use the given graph of the quadratic function f to write its formula as f() = a( - h) + k. ) - - - - 6 7 - - - Determine the verte of the graph of f. ) a) f() = ( - ) b) f() = -( + ) - 6 c) f() = ( + ) + d) f() = - 0 + e) f() = - + - Write the equation as f() = a( - h) + k. Identif the verte. ) f() = + 6 - ) - - - - - 6 7 8 - - - - -6-7 -8
Math, Review for Test Page Find f() = a( - h) + k so that f models the data eactl. 6) - - - 0 - - Solve the quadratic equation. Give eact, simplified answers, not decimals. 7) - 8 + = 0 The graph of f() = a + b + c is given in the figure. Determine whether the discriminant is positive, negative, or zero. 9) 8) 8 = 9) = 6 0) (p + 6) = - - - - ) + + = Solve b completing the square. ) a - a + 0 = 0 60) ) + = 7 ) = - 6 - - - Use the discriminant to determine the number of real solutions. ) s - s - = 0 6) t - 8t + 6 = 0 - The graph of f() = a + b + c is given in the figure. Solve the equation a + b + c = 0. 6) 7) w - w + 6 = 0 8) (- + ) = 6 0 0 0 - - - -0-0 -0
Math, Review for Test Page 6) 68) A grasshopper is perched on a reed 6 inches above the ground. It hops off the reed and lands on the ground about. inches awa. During its hop, its height is given b the - - - equation h = -0. +.0 + 6, where is the distance in inches from the base of the reed, and h is in inches. How far was the grasshopper from the base of the reed when it was.7 inches above the ground? Round to the nearest tenth. - Graph the quadratic function. Identif the following: i) the verte, ii) the ais of smmetr, iii) the -intercept, iv) the -intercept(s), if an. 6) a) f() = - + b) g() = -( + ) + 6 c) h() = - - 6) A ball is tossed upward. Its height after t seconds is given in the table. Time (seconds) 0... Height (feet) 6. 9... 0. Find a quadratic function to model the data. Use the model to determine the following: a) when the ball reaches its maimum height, b) the maimum height. the ball reaches. 6) A farmer has 900 feet of fence with which to fence a rectangular plot of land. The plot lies along a river so that onl three sides need to be fenced. What is the largest area that can be fenced. 66) A rock falls from a tower that is 00 feet high. As it is falling, its height is given b the formula h = 00-6t. How man seconds will it take for the rock to hit the ground? 67) A ball is thrown downward from a window in a tall building. Its position at time t in seconds is s = 6t + t, where s is in feet. How long (to the nearest tenth) will it take the ball to fall 6 feet? Simplif the epression using the imaginar unit i. 69) a) -6 b) -7 c) - Perform the indicated operation and write the epression in standard form. 70) a) ( - 7i) + (6 + i) b) (9 + 8i) - (-6 + i) c) i( - i) d) (8 + i)( - i) Multipl and write the result in standard form. 7) (7 - -)( + -9) Divide and write the result in standard form. 7) a) 9 + i - i b) + i + i Solve the quadratic equation. Write comple solutions in standard form. 7) a) + + = 0 b) - 8 + = 0 c) ( + ) = - Complete the following for the given f(). (i) Find f( + h). (ii) Find the difference quotient of f and simplif. 7) a) f() = - 8 b) f() = + - 9 Find the difference quotient for the function and simplif it. 7) a) f() = - 8 b) g() = + -
Math, Review for Test Page 6 Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 76) Provide the requested response. 8) For the function g() = if - - + 6 if < a) Find g(-) b) Find g(0) c) Graph the function d) What is the domain of g? - - - - - - - - Graph f. Use the graph to determine whether f is continuous. 8) -- if - 0 f() = - if 0 < < - if Identif where f is increasing and where f is decreasing. 77) a) f() = - b) f() = + 78) The distance D in feet that an object has fallen after t seconds is given b D(t) = 6t. (i) Evaluate D() and D(). (ii) Calculate the average rate of change of D from to. Interpret the result and include appropriate units of measuer. Write a formula for a linear function f that models the data eactl. 79) - - 0 f() 6 - - Write a formula for a linear function f whose graph satisfies the conditions. 80) Slope:.; passing through (,.) 8) In a certain cit, the cost of a tai ride is computed as follows: There is a fied charge of $.8 as soon as ou get in the tai, to which a charge of $.8 per mile is added. Find an equation that can be used to determine the cost, C(), of an -mile tai ride.
Answer Ke Testname: CAREVIEW_F ) a) = -( - 7) + b) = 8( - ) + ) = - - ) = + 8 ) = + 8 ) = 7 + 7 6) = 7 8 + 7) = -7 8) = 9) 60 sec - - ) ) a) Linear b) Nonlinear c) Linear ) 8 ) 7 ) 7 ) 9 66 - - 6) All real numbers 7) a) Contradiction b) Identit c) Conditional 8) f() = 8 9) 8 m 0) Width: 0 in.; length: 6 in. ) [, ) ) a) (-, ) b) (-, 9] c) (-, ) ) a) (, ] b) [- 8 9, ] ) { 9} ) -, 6), - 7), - 6 8) No solution 9 9),- 0) ) i) = ; ii) { < } or (-, ) ) a) - 7, 9 b) (-, -) (, ) c) [-7, -] ) (-, -) (, ) ) - 7, - ) i) The monthl averages are alwas within of 8 F. ii) {T T 6} 6) a) Linear b) Quadratic; c) Neither d) Linear 7) a) b) 8) a > 0 Verte: (, -); Ais of smmetr: = Increasing on [, ) Decreasing on (-, ] 9) a < 0 Verte: (-, ) Ais of smmetr: = - Increasing on (-, -] Decreasing on [-, ) 0) [-, ) ) a) (, 0) b) (-, -6) c) (-, ) d) (, ) e) (, -) ) f() = ( + ) - ; (-, -) ) a) a > 0 b) a < 0 ) f() = ( - ) - ) f() = -( - ) - 6) f() = -( + ) + 7), 8) 0, 9) ± 0) -6 ± ) - ± ), ) - ± ) - ± ) Two real solutions 6) One real solution 7) No real solutions 8) Two real solutions 9) Negative 60) Positive 6) 0, -9 6)
Answer Ke Testname: CAREVIEW_F 6) a) i) verte: (0, ) ii) ais of smmetr: = 0 iii) -intercept: (0, ) iv) -intercepts: (-, 0), (, 0) - - - - b) i) verte: (-, 6) ii) ais of smmetr: = - iii) -intercept: (0, ) iv) -intercepts: (-+ 6, 0), (-- 6, 0) - - - - c) i) verte: (, -9) ii) ais of smmetr: = iii) -intercept: (0, -) iv) -intercepts: (-, 0), (, 0) 6),0 ft 66) sec 67).9 sec 68) 8. inches 69) a) 8i b) i 7 c) i 70) 8 - i + 7i + 8i - i 7) + i 7) 9 + 0 i 7) a) - ± i b) ± 6i c) - ± i 7) a) (i) + h - 8 (ii) b) (i) + 8h + h + + h - 9 (ii) 8 + h + 7) a) + h - 8 b) 6 + + h 76) increasing: [-, 0] [, ); decreasing: (-, -] [0, ] 77) a) increasing: (-, ); decreasing: never b) increasing: [0, ); decreasing (-, 0] 78) (i) D() = 6, D() = 00 (ii) ; the object's average speed from to seconds is ft/sec. 79) f() = - + 6 80) f() =. +.9 8) C() =.8 +.8 8) a) g() = b) g() = c) 8 6 - -8-6 - - 6 8 - - -6-8 - d) domain: [-, ] - - - - - - 8) Not continuous - - - - - - - - 6) The ball reaches a maimum height of.6 feet in.6 seconds.