# Solve the attached review test questions

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Mathematics

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Please see the attached PDF file and Solve each question step by step.

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MULTIPLE CHOICE- Choose the one alternative that best completes the statement or answers the question. Find the equation that the given graph represents. 1) 1) -10 A)P(x)=-*3* 4x2+x-5 C) P(x):15 * 4*3 - x2 + 3x - 5 B)P(x)=x3+x2+x+5 D)P(x):x3+ 4;p- x-5 SHORT ANSWER- Write the word or phrase that best completes each statement or answers the question. Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. 2) t(x) = x3 - 7x2 +15x - 25 Determine whether the statement is true or false. 3) If f(x) is a polynomial and f(-5) = O then x + 5 is Z) _ a factor of f(x). 3) Sketch the graph of the polynomial function. a)f(x):(x+2)3-l 4) Find the correct end behavior diagram for the given polynomial function. 5)P(x)=-x5-3x3-8x+1 s) \ \ Use the graph to answer the question. 6) Find the domain and range of the rational function graphed below. -10 -8 -6 -4 -2 I 6) .1 68 t- ----------t-' ------..- i I \ \r in \t, r' liro MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine which of the rational functions given below has the following feature(s). 7) The x-intercept is (5, 0) A)f(x)=# sir(*r =i* c)f(x)=# 7) D)f(x):** 8) The y-intercept is (0, 4) 6tt*l:# 8) B)f(x):# c)f(x):i3 D)f(x):# 9) There is a "hole" in its graph at x = 5 e) f(x):i* A)f(x)=# B) c)r(x)=#I (x + dr rr*r _ - 5Xx 9) (x+5)(x-5) 10) The x-axis is its horizontal asymptote A)f(x) v =- LL) x-intercepts: (-3, 0) and (3, 0), asymptote: y = 6(,):* B)f(x):# -) 10) D)f(x) =# y-intercept[O 9) vertical asymptotes: x : -]" and x = 1, horizontal 1 (x + 3Xx - 3) A) f(x) _ (x+1)(x-1) (x + O f(x) _ - 3)(x 3) (x-1)(x+1) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Answer the question 12) How can the graph of f(x) =* be obtained from the graph of y 2 = 1 7 12) 11) Give the domain and range for the rational function. Use interval notation. L 13) f(x) - ( 1 13) (x + 4)2 Give the equations of any vertical asymptotes. r1) f(x)=# 74) 1s)f(x):* 1s) Give the equations of any horizontal asymptotes. 16)g(x)=# 17)h(x) =9xz 'l*' 18)s(x) =# 1b) 17) -8 18) Give the equation of any oblique asymptotes. 19) h(x) -6 - 5x+2 = 3xzlx 7e) 20)f(x)=# 20) Identify any vertical, horizontal, or oblique asymptotes in the gfaph of y= f(x). State the domain of f. 27) 21) -10 -8 -6 -4 -2 J \ \ Sketch the graph of the rational function. 22) f(x)=:+ 22) Solve the problem. 23) If the average cost per unit C(x) to produce x units of plywood is given what is the unit cost for ty C(x)=ffi, 23) 20 units? Determine whether or not the function is one-to-one. 24) 24) 2s) 4 \ Decide whether the given functions are inverses. 26) f = lF3, -6), (0,4), (4, -3), (8, 10)l g= le6, -3), (4,0),(-3,4), (10, 8)) 26) Use the definition of inverses to detennine whether f and g are inverses. 27)t(x)=2x-4, 28) f(x) =7x -7, g\$)=+ g(*) =|* 27) *1 28) If the function is one-to-one, find its inverse. If not, write "not oneto-one." 29) l(L9,5), (1O -L), (-19,7)l 2e) 30) l(-7, -7), (-6, -7), (-5, -3), (-4, -9\l 30) 31) f(x) =6x3 + 4 31) 32) f(x) 32) =2x+3 Find the function value. If the result is irrational, round your.rnswer to the nearest thousandth. 33) Let f(x):4x. 34) Let (.):f+l..Find Find f(3). 33) (3). 34) L'J Evaluate the logarithm. 3s) log, 1 fr 35) Write an equivalent expression in exponential form. 36) log' 625 =4 36) Write in logarithmic form. 3n 2-2 :! J/) Solve the equation. 38)tos7\$=x 38) Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. 39) 1o9614x6y) 3e) 5 Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a+1and b*L. 40) (logn x - logs y) + 5 logx z 40) Solve the system by substitution. 41)x+Y=-2 41) x-Y=-8 Solve the system by elimination. 42) x- 3y:-8 6x - 4Y =)/ 42) Solve the system by substitution. 43) x+7y=27 13) 6x+7Y=\$/ If the system has infinitely many solutions, write the solution set with x arbitrary. 44)5x-8y=1 Solve the system. -10x + 1'6Y Write the augmented matrix for the system. Do not solve the system. 45) 7x+ 4y= J) 5x+ 3Y: 46) 6x )) +22= 1.0 4y+72= 26 9x + 3y 44) =1 +72: 4s) 46) 32 Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, give the solution with y arbitrary. 47)x+y=J 47) *-Y=-4 Use the Gauss-|ordan method to solve the system of equations. variable be the arbitrary variable. 48) 7x-9y- z=-24 x-3y-52=-54 -2x+ y+ z= 7 If the system has infinitely many solutions, let the last 48) Find the value of the deterninant _r) 4e) l:;l ls+t 50)lasz s0) lr+s 6 \ 1314 REVIEW TEST4 FpJ-LZOI7 1)D 2) 5,7 + 2i,7 3) True - 2i 4) v.......... ..".....5 r'l . l.* ...t, '- -'5' . 5) *o 6j Domain: (--, -2) u (-2, *\ Range: (--, -3) u (-3' -) 7)B 8)A e)D 10) 11) c A By making a horizontal shift of 6 units to the right 13) Domain: (--, -4) v (-4, *\ Range: (0, -) 12-) 14) x 2 =-f, 15)x=3,x=-3 16) none 17)y=3 18)y=0 19) none 20)y=1ag 21) Vertical: x =2;horizontal: y = -4; ('*,2) u (2' *) 22) .-lA -.8. -.6. 23) \$18.00 24) No 7 \ Answer Key Testname: MATH 1314 REVIEW TEST4 FALLZOIT 25) Yes 26) Yes 27) No 28) Yes 29) l(5 , 79) , (-7 , 70), (7 , -79)l 30) not one-to-one 31) f-1(x) = 32) f-1(x) zffi ^l\l6 =+ 33) 64 zqt1:rx 3s) -2 36) 54 = 625 37) togrj.=-z 38) {-2} 39) logu4 + 6logax + logaY 4o)rog2ttrl 41) {(-5,3)} 42) \V,s)l 43) t(6,3)) 44) a 4s) 46) tliE l l":-l;21 lo z zlzz l 44{- +,+\ 48) {(3,4,9)l 4e) 62 s0) 6 8
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