Chapter 1 and 13 Math 1 Practice set Note: the actual test differs. Given f() and g(), find the indicated composition. 1) f() = - ; g() = 3 + Find (f g)(). Determine whether the function is one-to-one. If so, find a formula for the inverse. 8) h() = 3-1 ) f() = + ; g() = 9 + Find (g f)(). 3) f() = + 8; g() = + 8 Find (f g)(). Given f() and g(), find the indicated composition and evaluate. ) f() = 3 + 6; g() = Find (g f)(3). ) f() = ; g() = - 1 Find (f g)(11). Determine whether the function is one-to-one. If so, find a formula for the inverse. 9) g() = - 3 ) g() = 8 + 9 Determine whether the function is one-to-one. Give a valid reason. 6) f() = 6-6 For and 6 Determine whether the function is one-to-one. If so, find a formula for the inverse. 11) h() = 3 + 7 Determine whether the function is one-to-one. Give valid reason. 7) f () f Determine whether the function is one-to-one. If so, find a formula for the inverse. 1) f() = - 9 Graph the function using a solid line and its inverse using a dashed line on the same set of aes. 13) f() = - 6 - - - - 1
1) f() = + Graph. 18) = ( + 1) - - - - - - - 6 - - For the function f, use composition of functions to show that f -1 is as given. 1) Let f() = + 3. Show that f-1 = 3 -. 16) Let f() = 3 -. Show that f -1 () = 3 +. Graph. Label at least two points on each graph. 17) = - - 6 - - Solve the problem. 19) The amount of particulate matter left in solution during a filtering process decreases Simplif. b the equation P = 600 (0.). 6 n, where n is the number of filtering steps. Find the amounts left for n = 0 and n =. (Round to the nearest whole number.) 0) log 1 1) log 1 ) log 8 3 3) log 0.01 ) log 6 6 ) log 6) log 8 1
Graph. 7) = log 3) z = 8 Solve the problem. 36) log 8 = 37) log = - - 6 - - 38) log 1 = 39) log = -3 Graph. Label at least two points on the graph. 8) = log 1/ - - 6 - - 0) log 6 = 3 Epress as a sum of logarithms. 1) log 6 () ) log (z) Epress as a single logarithm. 3) log 6 1 + log 6 1 ) log 11 + log 1 Rewrite as an equivalent eponential equation. Do not solve. 9) log = Epress as a product. ) log 7 9 6) log c Z - 30) log 6 36 = 31) log 3 1 9 = - 3) log = 0.301 Rewrite as an equivalent logarithmic equation. Do not solve. 33) 3 = 8 3) 83,3 1/7 = 7 Epress as a difference of logarithms. 7) log g M 67 Epress as a sum, difference, and product of logarithms, without using eponents. 8) log 1 13 r s 9) log b m p 8 n 9 b 3
Epress as a single logarithm, and, if possible, simplif. Simplif. 0) loga + 1 log a z 1) 1 log a + 6 loga - loga ) 1 log a + loga - 3 loga 3) logw ( - 6) - logw ( - 8) ) log a a 09 ) log e e Solve. Where appropriate, include approimations to the nearest thousandth. If no solution eists, state this. 6) ( - ) = 6 7) 8 = 16 ( + ) 8) = 6 9) 9 = 81 ( + 9) 60) log = 1 Solve the problem. 66) Yearl sales of an electronic device S(t), in millions of dollars, t ears after 1997 can be estimated b S(t) = 00 t. What is the doubling time for the earl sales? 67) Find the hdrogen ion concentration of a solution whose ph is.6. Use the formula ph = -log [H + ]. 68) Suppose that $6000 is invested in an account where interest is compounded continuousl at 3.7% per ear. What is the balance after 1 ear? after ears? 69) Suppose that $7000 is invested in an account where interest is compounded continuousl at 3.% per ear. What is the doubling time? Solve. 70) How long will it take for the population of a certain countr to triple if its annual growth rate is 3. %? (Round to the nearest ear.) Choose the equation that matches the graph. 71) 61) log - log( + 7) = 1 6) log ( - 8) + log ( - 8) = 1 - - - 63) ln - ln ( - 6) = ln 6) ln ( - 6) + ln ( + ) = ln 6) ln ( - ) + ln ( + ) = ln 36 - A) ( - 1) + ( - ) = B) ( - 1) - ( - ) = 16 C) ( - 1) + ( - ) = D) ( - 1) + ( - ) = 16
Graph. Be sure to label the verte. Round to the nearest hundredth if necessar. 7) = - 7) = + 3 - - - - - - - - - Graph. Be sure to label the verte and at least one other point on the graph. Find an equation of the circle satisfing the given conditions. 76) Center at (, 7), radius 6 77) Endpoints of a diameter: (, -) and (, 1) 73) = 1 Graph. Label the intercepts. 78) + 9 = 1 - - - - Graph. Be sure to label the verte. Round to the nearest hundredth if necessar. 7) = - Graph. 79) + 6 = 1 - - - - - -
80) 8 + - 18 = 0 - - 81) 9( - ) + ( + 1) = 8) 6-1 = 1 A) A horizontal ellipse. B) A hperbola with a horizontal ais C) A hperbola with a vertical ais. D) A vertical ellipse. 86) ( - 7) + ( + 1) = A) A circle with its center at the origin. B) An ellipse with its center at the origin. C) A circle with its center not at the origin. D) An ellipse with its center not at the origin. 87) - = A) A parabola opening to the right or left. B) A vertical ellipse. C) A hperbola with a vertical ais. D) A parabola opening upward or downward. - - - - Find the equation in standard form of an ellipse centered at the origin that passes through the given points. 8) (-, 0), (, 0), (0, -9), and (0, 9) 88) ( - ) + ( + ) 16 = 1 A) A circle with its center not at the origin. B) A hperbola with its center not at the origin. C) An ellipse with its center not at the origin. D) A parabola with its center not at the origin. 83) (-3, 0), (3, 0), (0, - ), and (0, ) Choose the description that matches the equation of the conic section. 8) 6-36 = 1 A) A hperbola with a horizontal ais. B) A horizontal ellipse. C) A hperbola with a vertical ais. D) A vertical ellipse. Graph. Label the intercepts 89) 36 - = 1 - - - - 6
Graph. 90) 16 - = 6 9) - = 1 9) 16 = + 6 96) = 16 - - - - - 91) 9-6 = 18 97) = 6 Find the vertices of the hperbola. 98) - 36 = 900 Find the asmptotes of the hperbola. 99) - 00 = 1 Solve. 0) + = 1 - = 1 - - - - 9) = - - 1) + = 0 - = ) - = -0 - = 3 3) + + = 0 + = 3 ) - = 1 = 3 ) + - = 36 + + = 1 - - 6) + = 36 - = 36 Classif the following as the equation of a parabola, a circle, an ellipse, or a hperbola. 93) + = 7
Answer Ke Testname: 1CH1&13P 1) (f g)() = 9 + + 1 ) (g f)() = 18 + + 3) (f g)() = + 16 ) 1 ) 30 6) No 7) Yes 8) h -1 () = + 1 3 9) Not a one-to-one function ) g -1 () = 9-8 11) h -1 () = 3-7 1) f -1 () = + 9, 0 13) - - - - 1) - - - - 1) 1. (f -1 f)() = f -1 (f()) = f -1 + 3. (f f -1 )() = f(f -1 ()) = f(3 - ) = = 3 + 3 (3 - ) + 3 - = ( + ) - = ; = 3 3 = 8
Answer Ke Testname: 1CH1&13P 16) 1. (f -1 f)() = f -1 (f()) = f -1 ( 3 - ) = 3 ( 3 - ) + = 3 3 = ;. (f f -1 )() = f(f -1 ()) = f( 3 + ) = 17) 3 + 3 - = + - = - - 6 - - 18) - - 6 - - 19) 600, 7 0) -1 1) - ) 3 3) - ) ) 6) 3 9
Answer Ke Testname: 1CH1&13P 7) - - 6 - - 8) - - 6 - - 9) = 30) 6 = 36 31) 3 - = 1 9 3) 0.301 = 33) 3 = log 8 3) 1 7 = log 83,3 7 3) z = log 8 36) 3 37) 38) 0 1 39) 1 0) 16 1) log 6 + log 6 ) log + log + log z 3) log 6 1 ) log 13
Answer Ke Testname: 1CH1&13P ) 9 log 7 6) - log c Z 7) log g M - log g 67 8) log 1 13 + 1 log 1 r - log 1 s 9) log b m + 8log b p - 9log b n - 0) loga ( z 1/ ) 1) loga 6 7/ ) loga / 3) logw ( + 8) ) 09 ) 6) 7) - 8 8) -3, 1 9) No solution 60) 61) No solution 6) 63) 1 6) 9 6) 7 66) 1.0 r 67).1-6 68) $66.16; $660.8 69) 0. r 70) 3 ears 71) D 7) (0, 0) - - - - 11
Answer Ke Testname: 1CH1&13P 73) (0, 0) - - - - 7) (-, 0) - - - 7) - 6., - -1.0) - - - 76) ( - ) + ( - 7) = 6 77) - 9 + + 3 13 = 1
Answer Ke Testname: 1CH1&13P 78) 79) - - 80) - - 13
Answer Ke Testname: 1CH1&13P 81) - - - - 8) 16 + 81 = 1 83) 18 + = 1 8) A 8) C 86) C 87) D 88) C 89) - - - - 1
Answer Ke Testname: 1CH1&13P 90) - - - - 91) - - - 9) - - - - - 93) Circle 9) Parabola 9) Hperbola 96) Circle 97) Hperbola 98) (0, 6), (0, -6) 99) = 3, = - 3 0) (9, 8), (-8, -9) 1
Answer Ke Testname: 1CH1&13P 1) (0, ), (-,0) ) (, 1) and -8, - 11 3) (0,0) 300 9, - 90 9 ) (3, 1), (-3, -1) ) (9, 3), (-9, 3), (3, 9), (-3, 9) 6) (6, 0) and (-6, 0) 16