MSTH 236 ELAC SUMMER 2017 CP 1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 MSTH 236 ELAC SUMMER 2017 CP 1 SHORT ANSWER. Write the word or phrse tht best completes ech sttement or nswers the question. Find the product. 1) (8y + 11)(4y 2-2y - 9) 1) Simplify the expression by combining like terms, if possible. 2) -4(9r + 2) + 7(4r + 6) 2) Fctor the GCF from the polynomil. 3) 6x 7 y 6 z - 10x 6 y 5 3) Fctor completely using grouping. 4) 14y2 + 63y ) 5) Fctor by grouping: 12x 3-8x 2 + 3x - 2 5) 6) Fctor using integer coefficients: 4x 3 y 2-20x 3 y + 25x 3 6) 7) Perform the indicted opertion nd reduce to lowest terms: 3x + 3y x 2-5xy - 14y 2 6x + 6y x 2 + 9xy + 14y 2 7) 8) Combine into single frction nd simplify: y - 5 y y + 5 y y y 8) 9) Express s simple frction reduced to lowest terms: b - 1-2b b b 9) Simplify. The exponents in the nswer should be positive integers. 10) (6x -3 y 5 )(6-1 x 6 y -8 ) 10) 11) Write 3x3 (x -2) 3-2x 2 (x - 2) 4 (x - 2) 2 with positive exponents only, nd s single frction reduced to lowest terms. 11) 12) Write in stndrd nottion. 12) 1

2 13) According to the 2000 U.S. census, the popultion of the United Sttes on April 1, 2000 ws pproximtely 281,422,000 (Source: The popultion of the U.S. in 1900 ws pproximtely 76,212,000. Write both popultion numbers in scientific nottion nd use these expressions to clculte the rtio of the popultion in 2000 to tht in Express the rtio in stndrd deciml form to four deciml plces. 13) 14) Simplify nd express using positive exponents: 4x 2/3 10x -1/4-1 14) 15) Write in simplest rdicl form: 5 243x 13 y 22 15) 16) Chnge to simplest rdicl form: 12m 8 n 6 3m 8 n 2 16) Rtionlize the denomintor nd simplify. Assume tht ll vribles represent positive rel numbers. 2 17) 17) ) Solve by fctoring: 4y 2 = 10y 18) Use the squre root property to solve the eqution. 19) (x + 3)2 = 44 19) Use the qudrtic formul to solve the eqution. 20) x2 + 10x + 10 = 0 20) 21) Fctor, if possible, s the product of two first-degree polynomils with integer coefficients: 4x 2-131x ) Use point-by-point plotting to sketch the grph of the eqution. 22) y = x ) 23) The supply nd demnd equtions for certin product re s = 2,500p - 14,500 nd d = 3,000, where p is the price in dollrs. Find the price where supply equls demnd. p 23) 2

3 Determine whether the grph is the grph of function. 24) 24) Determine whether the reltion represents function. If it is function, stte the domin nd rnge. 25) 25) ) {(-2, 8), (-1, 5), (0, 4), (1, 5), (3, 13)} 26) Use point-by-point plotting to sketch the grph of the eqution. 27) f(x) = 2x x ) Find the function vlue. 28) f(x) = x2 + 7 x 3 ; f(4) 28) + 6x 29) Given tht f(x) = 5x 2-2x, find f(t + 2). 29) 30) If g(x) = -4x 2 + x - 9, find g(-2), g(1), nd g ) 31) For f(t) = 3-5t, find f( + h) - f(). 31) h Compute nd simplify the difference quotient f(x + h) - f(x), h 0. h 32) f(x) = 5x 2 + 7x 32) 3

4 Determine the domin of the function. 33) f(x) = - 7x ) 34) f(x) = 3 - x 34) 35) f(x) = 8 x 3 35) Solve the problem. 36) The point t which compny's costs equls its revenue is the brek-even. C represents cost, in dollrs, of x units of product. R represents the revenue, in dollrs, for the sle of x units. Find the number of units tht must be produced nd sold in order to brek even. C = 15x + 12,000 R = 18x ) Give the domin nd rnge of the function. 37) s(x) = 3 - x 37) 38) r(x) = x ) Grph the liner eqution nd determine its slope, if it exists. 39) 3x + 5y = 11 39) Find the slope nd y intercept of the grph of the eqution. 40) y = 5 2 x ) Write n eqution of the line with the indicted slope nd y intercept. 41) Slope = 5 2 ; y intercept = ) For the given function, find ech of the following: (A) Intercepts (B) Vertex (C) Mximum or minimum (D) Rnge 42) f(x) = (x + 4) ) Find the vertex form for the qudrtic function. Then find ech of the following: (A) Intercepts (B) Vertex (C) Mximum or minimum (D) Rnge 43) f(x) = x 2 + 4x ) 4

5 Answer Key Testnme: MATH236CP1 1) 32y y 2-94y ) -8r ) 2x 6 y 5 (3xyz - 5) 4) 7(2y - 1)(y + 5) 5) (3x - 2)(4x 2 + 1) 6) x 3 (2y - 5) 2 x + 7y 7) 2(x - 7y) 8) 3y2-14y - 12 (y + 2)(y - 2) 2 9) + b - b 10) x3 y 3 11) x 2 (x - 2)(x + 4) 12) 72,140,000 13) , ; ) 2x 11/12 15) 3x 2 y 4 5 x 3 y 2 16) 6m 8 n 4 17) ) y = 0 or ) { , } 20) {-5-15, } 21) (4x - 15)(x - 29) 22) 23) $6 24) not function 5

6 Answer Key Testnme: MATH236CP1 25) function domin: {3, 4, 5, 6} rnge: {15, 20, 25, 30} 26) function domin: {-2, -1, 0, 1, 3} rnge: {8, 5, 4, 13} 27) 28) ) 5t t ) -27, -12, ) -5 32) 10x + 5h ) All rel numbers 34) x 3 35) All rel numbers except 0 36) ) Domin: (-, 3]; Rnge: [0, ) 38) Domin: ll rel numbers; Rnge: [- 2, ) 39) slope:

7 Answer Key Testnme: MATH236CP1 40) Slope = 5 2 ; y intercept = ) y = 5 2 x ) (A) x-intercepts: - 7, -1; y-intercept: 7 (B) Vertex (-4, -9) (C) Minimum: -9 (D) y -9 43) Stndrd form: f(x) = (x + 2) 2-9 (A) x-intercepts: - 5, 1; y-intercept: -5 (B) Vertex (-2, -9) (C) Minimum: -9 (D) y -9 7