Torrence's Math Pages

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Torrence's Math Pages

Basic Algebra

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Syllabus

HW Answers/Copies of Assignments

Keys to extra practice sheets

Week 11:

 

 

Week 9 :

3.1.1 (10/31/17)

1.  b (show work!)

2a. 5^16 – again make sure that you show work

b. subtract exponents when dividing powers

3-9 y=10x+150

3.1.1b (11/1/17)

3-6. See below:

  1. 1/h^2
  2. x7
  3. 9k10
  4. n8
  5. 8y3
  6. 28x3y6

3-7. See below: 

  1. incorrect,  x100
  2. correct
  3. incorrect,  8m6n45

3-8

Make sure that you graph is sloping downward, that your graph has a y-intercept of (0,3) and that you are going down 1 right 2 for additional points.

3.1.2a (11/2/17)

3-19.   b, c, d, f

3-20. See below:

  1. 1/4
  2. 1
  3. 1/5^2 = 1/25
  4. 1/x^2

3-22. See below:

m = −1/3

y = −(1/3)x − 2

3-23. Let x = number of weeks.   1500 − 35x = 915; x = 17 weeks

3-24. y = 3x −

Week 8 key

Week 7 key

Week 5 – basic alg week 5 hw answers

2.2.2a Thursday, 10/5

2-59. y = 2x + 3

2-62. See table below and graph right.  x-intercept: (2, 0),  y-intercept: (0, –10)

x y
–2 –20
–1 –15
0 –10
1 –5
2 0

2-64.

Wednesday 10/4

2-49. See below:

  1. −4/3
  2. (0, −5)
  3. y = −x − 5

2-51.  y = −4x − 3 

2-52.  Graphs (a) and (b) have a domain of all numbers, while graphs (a) and (c) have a range of all numbers.  Graphs (a) and (b) are functions.

Tuesday 10/3

2-42. See below. 

  1. m = –2
  2. m = 0.5
  3. undefined
  4. m = 0

2-44. See below. 

  1. m = , b= (0, –4)
  2. m = −, b= (0, 3) 
  3. m = 0, b= (0, –5)

2-48. See below: 

  1. 4
  2. 16
  3. y = 4x + 16
  4. It would get steeper.

Monday 10/2

2-41. See below. 

  1. m =1/2
  2. (0, −4).
  3. See graph.

2-43. No; when x = 12, y = 102, so it would have 102 tiles.

2-45. See below. 

  1. −18
  2. −4
  3. undefined
  4. −5

Week 4 –

Thursday, 9/28

2-31y = 4x + 4

2-32. See below: 

  1. Line ay = 2x − 2,   Line b:  y = 2x + 3
  2. It would lie between lines a and b, because its y-intercept is at (0, 1).
  3. It would travel downward but would have the same y-intercept as the line from part (b).

Wednesday, 9/27

2-22. y = 3x 

2-23. No solution; you cannot divide by zero.

2-24. m = 1/3

Tuesday, 9/26

2-19.  Possible response: It is a parabola because it has an x2-term.

  1. Justify your prediction by making a table and graphing yx2 – 1 on graph paper.
x -2 -1 0 1 2
y 3 0 -1 0 3

The graph will be an upward opening parabola with a vertex at (0, -1) and x-intercepts at (-1,0) and (1,0).

b. Yes, it’s a function. All of the x-values (inputs) have only one y-value (output).

c. Domain: All real numbers   Range: y ≥ –1

2-21. Answers vary.  (The key is that the growth is by three tiles each time and that the figure zero starts with 2 tiles.)

Monday, 9/25

1-6. See below:

  1. (sketch figures)
  2. It grows by two tiles each time.
  3. 1

2.

  1. domain x: –1, 1, 2  range: y: -2, 1, 2
  2. domain –1 ≤ x < 1 range: – 1 ≤ y <2
  3. domain x≥ –1   range y ≥ –1

Week 3 –

9/21 Thursday

Paragraph something like …

The graph of the function is U-shaped. The graph has two x-intercepts at (-2, 0) and another at (4,0). It has a y-intercept at (0, -8). The graph has a vertex at (1, -9) and this is also a minimum point, so the range of the function is y ≥ -9. All values of x are possible, so the range is all real values. The graph points upward at both the left end and the right end of the graph. The graph is symmetrical through the vertex.

9/20 Wednesday

2-9. (a) and (b) are functions because each only has one output for each input.

  1. D: all real numbers, R: 1 ≤ y ≤ 3
  2. D: all real numbers, R: y ≥ 0
  3. D: x ≥ −2, R: all real numbers

2-10. All graphs have lines of symmetry.  Graph (a) has multiple vertical lines of symmetry, one at each maximum and minimum; graph (b) has one line of symmetry at  x = 1; graph (c) has one line of symmetry at y = 1.

I. paragraph something like …The graph looks like a W. It has parts that are decreasing and parts that are increasing. It decreases until x =-1 an then turns to increasing until x = 1 then turns to decreasing until x=3 then turns to an increasing function from this point forward. It has symmetry and the line of symmetry is x = 1. It has two x-intercepts at (-1, 0) and (3, 0) and a y-intercept at (0, 2). There minimum value is y=0 and increases infinitely from this level, so the range of the function is y ≥ 0. All values of x are possible, so the domain is all real values.

9/19 Tuesday

1-81.  See below:

  1. yes
  2. –6 ≤ x ≤ 6 (x is possible between and including -6 to 6)
  3. –4 ≤ y ≤ 4 (y is possible between and including -4 to 4)

I. Paragraph something like…The function looks like a square root function. It is an increasing function over it entire domain. It has neither x- nor y-intercepts, but it does have a minimum point at (1,3). Its domain is that x can be greater or equal to 1 and its range is that y can be greater or equal to 3. The graph has a starting point at its minimum point (1,3) and then increases indefinitely as x gets bigger. The graph is not symmetrical.

9/18 Monday

1-78. See below:

  1. Not a function because more than one y‑value is assigned for  between –1 and 1 inclusive
  2. Appears to be a function
  3. Not a function because there are two different y-values for x = 7
  4. Function

1-79. See below:

a. Graph a: x-intercepts (–1, 0) and (1, 0), y-intercepts (0, –1) and (0, 4)

     Graph b: x-intercept (19, 0), y-intercept (0, –3)

     Graph c: x-intercepts (–2, 0) and (4, 0), y-intercept (0, 10)

     Graph d: x-intercepts (–1, 0) and (1, 0), y-intercept (0, –1)

b. The x-intercept is where the curve crosses the x-axis. The x-intercepts are exist where y = 0.  The y-intercept is where the curve crosses the y-axis. The x-intercepts are exist where x = 0.

I. Paragraph something like… The curve is a square-root graph. The function has y-intercept at the point (0, -1) and an x-intercept at (1,0). The point (0, -1) is also the minimum value and what could be considered a starting point. The domain starts at x=0 and is possible for all positive values of x. This function does not have any symmetry. It is an increasing function for all values of x.

Week 2 –

9/15 Friday

 

 

 

 

 

 

 

 

 

 

9/14 Thursday

1-60.  No, because …

9/13 Wednesday

9/12 Tuesday

1-47. Paragraph that highlights the following information: V-shaped graph, opening upward. As x increases, y decreases left to right until x = –2, then y increases. x‑intercepts: (–3, 0) and (–1, 0). y‑intercept: (0, 1). Minimum output of –1. Special point (vertex) at (–2, –1). Symetric across the line x = –2.

9/11 Monday

Week 1 –

9/9 Friday

1-18
b. $18
c. 8.4 gallons
d. Typical response: The line would get steeper.

1-22. See below:
a. Function A = 84, Function B = no solution
b. He cannot get an output of 0 with Relation A. He can get an output of 0 by putting a 4 in Function B.

9/8 Thursday

1-6 (make sure that you have the units)
a. 270 square feet
b. 28 · 23 = 644 square feet
c. 270 – 150 = 120 square feet
d. 52 feet

1-7
a. True
b. True
c. False
d. True

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