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Final Review Questions for College Algebra | MATH 0020, Study notes of Mathematics

Material Type: Notes; Class: COLLEGE ALGEBRA PART 2; Subject: Mathematics; University: University of Pittsburgh; Term: Unknown 1989;

Typology: Study notes

Pre 2010

Uploaded on 09/02/2009

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Math 0020 - Final Review Questions
1. Find the domain and range of the following:
(a) f(x) = xโˆ’4
x2โˆ’4(domain only)
(b) g(x) = โˆš2x+ 7
(c) h(x) = 3
โˆšx+ 2
2. Sketch a graph of the following:
(a) g(x) = x2+ 6x+ 8 (also find the vertex and x-intercepts)
(b) i(x) = log2(x+ 1) โˆ’2
(c) j(x) = 3โˆ’x+1 โˆ’2
3. Among all the pairs of numbers (x, y) such that 2x+y= 20, find the pair for which the sum of the squares
is minimum.
4. Sketch a graph of the following:
(a) a(x) = โˆ’1
x2+ 1
(b) b(x) = 2|x+ 2| โˆ’ 1
(c) c(x) = ๎˜šโˆ’x2โˆ’1,xโ‰ค1;
x2+ 1,x>1.
5. Suppose yvaries inversely as the cube of x, and that y= 0.005 when x= 10. What is ywhen x= 5?
6. If f(x) = x2โˆ’1 and g(x) = 12
x+1 .
(a) Find f(3) and g(3).
(b) Find (f+g)(3) and (fโˆ—g)(3).
(c) Find (fโˆ’g)(x) and (fโˆ—g)(x).
(d) Find (gโ—ฆf)(2).
(e) Find (gโ—ฆf)(x).
7. Find the inverse of the following functions.
(a) f(x) = xโˆ’1
3x+2
(b) g(x) = 3โˆ’x5
โˆ’9
8. Find the vertex form, the factored form, the axis of symmetry, and the vertex of f(x) = x2+ 5x+ 6
9. Solve x2โˆ’7x+ 10 = 0 by factoring *AND* by the quadratic equation.
10. Solve 10x+1 = 32xโˆ’1.
11. Solve (4
9)2x+1 = (3
2)3xโˆ’1
12. A population of 400 bacteria doubles every 3 hours .
(a) How many bacteria are there after 6 hours?
(b) Find asuch that P(t) = P0atmodels this population.
(c) Use this equation to find how many there are after 5.5 hours.
(d) Find ksuch that P(t) = P0ekt models this population.
(e) Use this equation to find how many there are after 2.5 hours.
13. Expand log( 5
q10x2
y3) completely.
14. Solve ln(x+ 1) + ln(x+ 4) = ln(x+ 2) + ln(x+ 5) for x.

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Math 0020 - Final Review Questions

  1. Find the domain and range of the following: (a) f (x) = (^) xx 2 โˆ’โˆ’^44 (domain only) (b) g(x) = โˆš 2 x + 7 (c) h(x) = โˆš^3 x + 2
  2. Sketch a graph of the following: (a) g(x) = x^2 + 6x + 8 (also find the vertex and x-intercepts) (b) i(x) = log 2 (x + 1) โˆ’ 2 (c) j(x) = 3โˆ’x+1^ โˆ’ 2
  3. Among all the pairs of numbers (x, y) such that 2x + y = 20, find the pair for which the sum of the squares is minimum.
  4. Sketch a graph of the following: (a) a(x) = โˆ’ (^) x^12 + 1 (b) b(x) = 2|x + 2| โˆ’ 1 (c) c(x) =

{ (^) โˆ’x (^2) โˆ’ 1 , x โ‰ค 1; x^2 + 1, x>1.

  1. Suppose y varies inversely as the cube of x, and that y = 0.005 when x = 10. What is y when x = 5?
  2. If f (x) = x^2 โˆ’ 1 and g(x) = (^) x^12 +. (a) Find f (3) and g(3). (b) Find (f + g)(3) and (f โˆ— g)(3). (c) Find (f โˆ’ g)(x) and (f โˆ— g)(x). (d) Find (g โ—ฆ f )(2). (e) Find (g โ—ฆ f )(x).
  3. Find the inverse of the following functions. (a) f (x) = 3 xxโˆ’+2^1 (b) g(x) = 3 โˆ’ โˆ’x 95
  4. Find the vertex form, the factored form, the axis of symmetry, and the vertex of f (x) = x^2 + 5x + 6
  5. Solve x^2 โˆ’ 7 x + 10 = 0 by factoring AND by the quadratic equation.
  6. Solve 10x+1^ = 3^2 xโˆ’^1.
  7. Solve ( 49 )^2 x+1^ = ( 32 )^3 xโˆ’^1
  8. A population of 400 bacteria doubles every 3 hours. (a) How many bacteria are there after 6 hours? (b) Find a such that P (t) = P 0 at^ models this population. (c) Use this equation to find how many there are after 5.5 hours. (d) Find k such that P (t) = P 0 ekt^ models this population. (e) Use this equation to find how many there are after 2.5 hours.
  9. Expand log( 5

โˆš (^10) x 2 y^3 ) completely.

  1. Solve ln(x + 1) + ln(x + 4) = ln(x + 2) + ln(x + 5) for x.