Honors Pre-Calculus Semester Review 0 Chapters to. (GC Selected Problems Onl!). Model the following situation with a linear equation in slope-intercept form. The gas tank in a truck holds gallons. The truck uses gallon per mile. a. + + + +. Find the slope-intercept form of the equation of the line through the point(, ) parallel to the line 7 9. 7 7 7 a. + + 7. Find the domain of the function: h( ). All real numbers such that ( ) a. ±, 0 ± ±, 0. (GC) Find the domain and range of the function: + a. Domain:(, ) Range: [ 0, ) Domain:( ),,, Range: [, ) Domain: [ 0 ) Range: (, ) Domain: [ ) Range: [ 0, ). Describe the transformation that occurs in the function. g ( ) ( ) a. Horizontal shift of, units to the right and vertical shift of units downward Horizontal shift of, units to the left and vertical shift of units downward Horizontal shift of, units to the right and vertical shift of units upward Horizontal shift of, units to the left and vertical shift of units upward f for and g( ) g a. + + + + +. Find ( ) 7. If and ( ) + f g a. 70 9 g, find ( )( ) +. Find the inverse of the function. f ( ) ( ) f f ( ) + a. ( ) + f None of these ( )
9. (GC) Write the equation of the quadratic function in standard form and find the verte of the graph. + a. f ( ) ( + ) ( ) Verte:(, ) Verte: (, ) f ( ) ( + ) ( ) Verte:(, ) Verte: (, ) 0. Find the right-hand and left-hand behavior of the graph of the polnomial function. + 7 a. Left rises. Left rises. Left falls. Left falls. Right falls. Right rises. Right rises. Right falls.. (GC) Use the Intermediate Value Theorem to determine an interval in which the function is guaranteed to have a zero. + 7 a.,,, 0,. Use long division to divide. ( + ) ( ) a. + + + +. Use the Rational Zero Test to determine all possible rational zeros of f. + + + a. 0, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ± ±, ±, ±, ±, ±, ± 7 ±, ±, ±, ±, ±, ±. (GC) For the following function, - is a zero of what multiplicit? + 7 a.. Simplif. i 9 a. i i. ( + i)( + i) a. + i i i i
7. ( + i) ( i) a. i + i + i + i. Divide and write the result in standard form. 9 + 9i 7i 7 7i 7 7i 9 + 7i 9 + 7i a. 9. (GC) Find all the zeros of the function. f ( ) + 7 + a. 7± 77 7± 79 7± 77 7± 79 0. (GC) While driving along the highwa ou spot a road sign warning of a % downgrade ahea At what angle of depression will ou descend? a.. 0. 0... Determine the domain of the function. 9 All real numbers such that ( ) a.,, 0,, 0. Find the horizontal asmptotes, if an, of the graph of + 7 a. 0 No horizontal asmptotes 7. (GC) Find the horizontal asmptote of the graph of 9 a. 0 9 0. Determine if the graph of the rational function has a slant asmptote. If it does, find the equation + 7 of the slant asmptote. + + a. + No slant asmptote
. Evaluate the epression without using a calculator. log a.. Condense the epression to the logarithm of a single quantit: log log ( ) 0 0 a. log 0 log 0 ( ) log 0 ( ) None of these 7. Solve for. + a.. (GC) Find the value of. ( + ) log log a. 0.7.00 0.00.00 π 9. (GC) If possible, find the supplement of the angle θ. π a. π π not possible 0. Find an epression that completes the fundamental trigonometric identit: cos( ) a. cos sec cos sec. Let θ be an acute angle. Use the given function value and trigonometric identities to find the indicated trigonometric function. If sec θ 0, find tan θ. a. 0. Given tan θ and sin θ > 0, find cos. θ a. cosθ cosθ cosθ. Find the amplitude and the period of the function. cosθ a. Amp.. Amp. -. Amp.. Amp. -. Period. Period. Period π Period π. sin
. Find the function that is represented b the graph: a. cot tan cot tan π π. Use the properties of inverse functions to evaluate the epression. sin arccos a.. Use the trigonometric substitution, to write the algebraic epression as a trigonometric function of π θ, where 0 < θ <. 9, cosθ a. sinθ 0sinθ + cosθ sin θ 7. cos t sec t a. cos t sec t. (GC) cos sin + sec + csc a. sin sec csc sin cos 9. Find the -values that are solutions of the equation. cos 0 π 7π 7π π π π a.,,, π, 7π 0. Find all solutions of the equation in the interval [ 0,π ) cot csc 0 π π π 7π π π 7π a.,, 0,, π,, π
. (GC) Find the domain of the function: a. 0 0. (GC) Use a graphing utilit to find an relative minimum or maimum values of the function. + 9 a. Relative minimum: (-, ) Relative minimum: (, -) Relative maimum: (, -9) Relative maimum: (-, ) Relative minimum: (, -) Relative minimum: (, -9) Relative maimum: (-, ) Relative maimum: (-, ). (GC) The following table shows the results of an eperiment to determine if there is a relationship between the number of hours of television watched (H) and the GPA (G) of students in high school. Use a graphing calculator to find the equation of the line which best fits the data and gives the GPA as a function of the number of hours of television watche Also, discuss whether or not the line is a good model for the data. GPA ( G).....9 a. G 099. H +., not a good model Hours of TV ( H).....7 G. H + 00., a good model G 099. H +., a good model G. H + 00., not a good model. (GC) The demand for motors depends on the price per motor. A manufacturer determines that the number of motors he can sell is d p + 0p 00 where p is the price per motor in dollars. At what price will the demand for motors be at a maimum? a. $0 $00 $9 $90. (GC) If $7000 is invested in a long-term trust fund with an interest rate of % compounded continuousl, what is the amount of mone in the account after 0 ears? a. $,90.9 $,7.9 $,7. $0,.0. (GC) Find the time required for an investment of $00 to triple if the interest rate of.% is compounded continuousl. a..90 ears. ears 0.7 ears. ears
7. (GC) The half-life of carbon- is 700 ears. Find the age to the nearest ear of a sample in which bt % of the radioactive nuclei originall present have decae Use the growth model a e where a a. ears ears 9 ears ears. (GC) Earl in the 900s, an airplane manufacturer was able to increase the time its planes could sta aloft b constantl refining its techniques. Use a graphing utilit to find an eponential equation that best models the data. Assume is the number of ears after 90 and is the time aloft in hours. a. 0.0(.9) Years after 90 Time aloft (h) 0..... 9. 0 0.. 9.9(0.0) 0.(.9) 9. (GC) A -foot ladder makes an angle of with the ground as it leans against a house. How far up the house does the ladder reach? a..7 ft.7 ft. ft 7. ft 0. (GC) A plane is miles north and 7 miles east of an airport. If the pilot wants to fl directl to the airport, what bearing should be taken? a. S 7.7 W S. W N 7.7 E N. E
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