College Algebra ~ Review for Test Sections. -. Use the given graphs of = a + b to solve the inequalit. Write the solution set in interval notation. ) - + 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 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(). Solve the inequalit graphicall. Epress the solution in set-builder notation. ) - + 6 Solve the equation. 6) r - = 7 7) b + 6-8 = 0 8) m + + = 9) t - + 9 = Solve the absolute value equation. ) - = + ) - 6 = - 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 (, ) Solve the problem. ) 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.
Math, Review for Test Page Identif f as being linear, quadratic, or neither. If f is quadratic, identif the leading coefficient a. 6) a) f() = - 7 Evaluate. b) g() = 8 + 7 c) h() = + d) j() = - 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) 9) -6 - - - - - 6 - - - -6 - - - - - 6 - - - 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 - The graph of f() = a + b + c is given in the figure. State whether a > 0 or a < 0. ) a) b) 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 + -
Math, Review for Test Page Use the given graph of the quadratic function f to write its formula as f() = a( - h) + k. ) - - - - 6 7 - - - ) = - 6 Use the discriminant to determine the number of real solutions. ) s - s - = 0 6) t - 8t + 6 = 0 7) w - w + 6 = 0 ) 8) (- + ) = 6 - - - - - 6 7 8 - - - -6-7 -8 The graph of f() = a + b + c is given in the figure. Determine whether the discriminant is positive, negative, or zero. 9) 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 0) 8) 8 = 9) = 6 0) (p + 6) = ) + + = Solve b completing the square. ) a - a + 0 = 0 ) + = 7
Math, Review for Test Page The graph of f() = a + b + c is given in the figure. Solve the equation a + b + c = 0. ) 0 0 0 ) 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. 6) A rock falls from a tower that is 00 feet high. As it is falling, its height is given b the formula h = -6t + 00. How man seconds will it take for the rock to hit the ground? ) -0-0 -0 7) 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. Simplif the epression using the imaginar unit i. 8) a) -6 b) -7 c) - Graph the quadratic function. Identif the following: i) the verte, ii) the ais of smmetr, iii) the -intercept, iv) the -intercept(s), if an. ) a) f() = - + b) g() = -( + ) + 6 c) h() = - - Solve the problem. ) An object is shot into the air. Its height after t seconds is given in the table. Time (seconds) 0 Height (feet) 76 88 68 6 a) Use s(t) = -6t + v o t + s o to model the data. b) When does the ball reaches its maimum height? c) What is the maimum height the ball reaches? Perform the indicated operation and write the epression in standard form. 9) a) ( - 7i) + (6 + i) b) (9 + 8i) - (-6 + i) c) i( - i) d) (8 + i)( - i) Multipl and write the result in standard form. 0) (7 - -)( + -9) Divide and write the result in standard form. ) a) 9 + i - i b) + i + i Solve the quadratic equation. Write comple solutions in standard form. ) a) + + = 0 b) - 8 + = 0 c) ( + ) = -
Math, Review for Test Page Use the given graph of f() = a + b + c to solve the specified inequalit. ) a) f() < 0 b) f() > 0 The given graph represents a translation of the graph of =. Write the equation of the graph. 9) ) a) f() 0 b) f() 0 Use transformations of the graphs of = or = to sketch a graph of f b hand. 60) f() = - - 6) f() = ( + ) - 6 6) f() = -( - ) - Use the accompaning graph of = f() to sketch the graph of the indicated equation. 6) = f() - Solve the inequalit. ) + - > 0 6) - - < 0 7) - + - 0 Use the given table for f() = a + b + c to solve the inequalit f() < 0. 8) - - -9-6 - 0 f() 0-7 -6-7 0
Math, Review for Test Page 6 6) = -f() Use the graph of f to determine the intervals where f is increasing and where f is decreasing. 7) - - - - - - 6) = f(-) - - (-, ) Identif where f is increasing and where f is decreasing. 7) a) f() = - b) f() = + Answer the question. (, -) 66) How can the graph of f() = - + be obtained from the graph of =? 67) How can the graph of f() = -6 + 9 be obtained from the graph of =? For the given representation of f, graph its reflection across the -ais and the -ais. 68) f() = - - 69) Line graph determined b the table -8 f() 6 - Solve the problem. 7) 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. 7) - - 0 f() 6 - Write a formula for a linear function f whose graph satisfies the conditions. 7) Slope:.; passing through (,.) Graph f. Use the graph to determine whether f is continuous. 76) -- if - 0 Complete the following for the given f(). (i) Find f( + h). (ii) Find the difference quotient of f and simplif. 70) a) f() = - 8 b) f() = + - 9 f() = - if 0 < < - if
Answer Ke Testname: CAREVIEW_F ) [, ) ) a) (-, ) b) (-, 9] c) (-, ) ) a) (, ] b) [- 8 9, ] ) i) = ; ii) { < } or (-, ) ) { -} (-, ) 6) -, 7), - 8), - 6 9) No solution 9 ),- ) ) 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 0) Positive ) 0, -9 )
Answer Ke Testname: CAREVIEW_F ) 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) ) a) s(t) = -6t + 60t + b) The ball reaches a maimum height after seconds. c) The ball reaches a maimum height of feet. ),0 ft 6) sec 7) 8. inches 8) a) 8i b) i 7 c) i 9) 8 - i + 7i + 8i - i 0) + i ) 9 + 0 i ) a) - ± i b) ± 6i c) - ± i ) a) { - < < } or (, ) b) { < - or > } or (-, -) (, ) ) a) { 7} or [, 7] b) { or 7} or (-, ] [7, ) ) < or > 6) - < < 7) All real numbers 8) - < < 0 9) = ( - ) + 60)
Answer Ke Testname: CAREVIEW_F 6) 6) (, ) (-, -) 6) 66) Shift it horizontall units to the left and reflect it across the -ais. 67) Stretch it verticall b a factor of 6, reflect it across the -ais, and shift it 9 units upward. 68) -ais: = - + + 8 6 6) -8-6 - - - 6 8 - -6-8 6) -ais: = + - 8 6-8 -6 - - 6 8 - - -6-8
Answer Ke Testname: CAREVIEW_F 69) -ais: 8 6-8 -6 - - - 6 8 - -6-8 -ais: 8 6-8 -6 - - 6 8 - - -6-8 70) a) (i) + h - 8 (ii) b) (i) + 8h + h + + h - 9 (ii) 8 + h + 7) increasing: [-, 0] [, ); decreasing: (-, -] [0, ] 7) a) increasing: (-, ); decreasing: never b) increasing: [0, ); decreasing (-, 0] 7) (i) D() = 6, D() = 00 (ii) ; the object's average speed from to seconds is ft/sec. 7) f() = - + 6 7) f() =. +.9 - - - - - 76) Not continuous - - -