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MATH 1314 Final Exam Review: Solving Equations and Graphing Functions, Lecture notes of Advanced Calculus

United Business InstituteAdvanced Calculus

A final exam review for a college-level mathematics course, covering various topics such as solving equations, simplifying expressions, finding roots, and graphing functions. Students are expected to show all work and justify answers for problems involving linear equations, quadratic equations, logarithms, absolute values, and polynomial functions.

Typology: Lecture notes

2021/2022

Uploaded on 08/05/2022

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Name: MATH 1314
FINAL EXAM REVIEW
SHOW ALL WORK AND JUSTIFY ALL ANSWERS.
Solve each of the following for x:
1. 4x+7=13 2. 5(x+2)โˆ’6(xโˆ’1) = 3(3xโˆ’7)
3. 7 โˆ’3(2โˆ’4x) = 10 โˆ’x4. 2xโˆ’9+x=21
5. x(x+3) = 10 6. 3xโˆ’1=5
x+1
7. 3 โˆ’4xโ‰ค17 โˆ’2x8. 3x=5 Round to 3 decimal places.
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Download MATH 1314 Final Exam Review: Solving Equations and Graphing Functions and more Lecture notes Advanced Calculus in PDF only on Docsity!

Name: MATH 1314

FINAL EXAM REVIEW

SHOW ALL WORK AND JUSTIFY ALL ANSWERS.

Solve each of the following for x:

  1. 4x + 7 = 13 2. 5(x + 2 ) โˆ’ 6 (x โˆ’ 1 ) = 3 ( 3 x โˆ’ 7 )
  2. 7 โˆ’ 3 ( 2 โˆ’ 4 x) = 10 โˆ’ x 4. 2x โˆ’ 9 + x = 21
  3. x(x + 3 ) = 10 6. 3x โˆ’ 1 = (^) x +^5
  4. 3 โˆ’ 4 x โ‰ค 17 โˆ’ 2 x 8. 3x^ = 5 Round to 3 decimal places.

Solve each of the following for x:

  1. log( 2 x โˆ’ 3 ) = log(x + 4 ) 10. log 9 x = โˆ’ (^12)
  2. x^10 +^3 = x^ โˆ’ x 1 12. | 3 x โˆ’ 4 | = 5
  3. 2x^2 = 7 x + 1 14. x^2 โˆ’ 6 x = โˆ’ 8
  4. x^2 โˆ’ x โˆ’ 6 > 0 16. 2 โˆ’ 5 x โ‰ค 18 โˆ’ x
  5. (x + 5 )^2 = 4 18. 2x^2 โˆ’ 2 x + 5 = 0
  1. Write the equation of the line passing through the point ( 1 , 5 ) and is perpendicular to the line 2x โˆ’ 3 y = 6.
  2. Find the domain of f (x) = โˆš 2 x โˆ’ 3 28. Find the domain of the function (^) x (^2) โˆ’^5 x 7 +x +^2 .
  3. If f (x) = 3 x โˆ’ 4, find f^ (x^ +^ h h)^ โˆ’^ f^ (x). 30. If g(x) = โˆš 2 + x, find gโˆ’^1 (x).
  4. If f (x) = 3 xโˆ’ 7 , find f โˆ’^1 (x). 32. f (x) = 2 x+7 and g(x) = 4 xโˆ’9, find ( f โ—ฆg)(x).
  5. If f (x) = 3 x + 4 and g(x) = โˆš 1 โˆ’ x, find (g โ—ฆ f )(x).

Sketch the following graphs. Show the coordinates of at least 3 points on each. Show any asymptotes as dotted lines.

  1. 5x โˆ’ 7 y = 35 35. f (x) = 3 โˆ’x
  2. y = |x| 37. h(x) = โˆšx + 1
  3. h(x) = (x โˆ’ 3 )^2 โˆ’ 1.
  4. Find the vertex of the parabola y = 2 x^2 + 16 x + 33 and graph the parabola.
  1. Solve the system of equations: 4 x + 5 y = 4 8 x โˆ’ 15 y = 3
  2. A man wants to put up a fence around his 16ft by 20ft swimming pool. He wants the border to be of equal width. If he has 154 feet of fencing, find the width of the border.
  3. An ancient cloth has a carbon-14 content that is 57% of that found in living wood. If the half-life of carbon-14 is 5700 years and the amount of radioactive material present at time t is given by A = A 02 โˆ’t/h^ where A 0 is the initial amount and h is the half-life, how old is the cloth?
  4. Fred leaves a party driving at 50 miles per hour. His friend George notices that Fred left his cell phone, so he drives after Fred at 60 miles per hour. How long will it take George to catch Fred if Fred had a 15 minute head start? (Warning!! Watch your units!!)
  1. If one leg of a right triangle is 14 feet shorter than the other leg, and the hypotenuse is 26 feet, how long are the legs?
  2. A business buys a copier for $1050. In 8 years, the copier will be worth $90. If y is the value of the copier after x years, find the equation of this line. How much will the copier be worth in 3 years?
  3. A farmer raises corn and soybeans on 350 acres of land. He will plant 100 more acres of corn than of soybeans. How many acres of each does he plant?
  4. Write as a matrix and solve using Gauss-Jordan elimination. 3 x โˆ’ 5 y = โˆ’ 25 2 x + y = 5
  5. Write as a matrix and solve using Gauss-Jordan elimination. 3 x + 6 y = 9 2 x + 6 y = 12