EN17 Introduction to Algebra, Week 5 by Chris Yang

chrisyang — 2016-10-26 09:42:15 UTC

1. Inequality symbols

chrisyang — 2016-10-26 09:46:47 UTC

Express x = -2, x ≥ -2, x ≤ -2, x > -2, x < -2, on number axis.

Exercise:
(1) Graph: -10 < x ≤ 15;

(2) Graph: y = 8, y < -5, 6 < x, x ≥ 0;

(3) Graph: |x| < 5, |y| ≥ 5.

3. Graphing quadratic functions

chrisyang — 2016-10-26 10:12:20 UTC

(1) Determine the vertex;
(2) Determine another two points symmetrical to the vertex;
(3) Draw a parabola that connects the vertex and two points.

chrisyang — 2016-10-26 10:25:28 UTC

1. Plot linear functions: f(x) = ax + b

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(1) Locate any two points on the function;
(2) Draw a line that connects the two points;

The graph of f(x) = x +5.

1. Plot linear functions

chrisyang — 2016-10-26 10:46:29 UTC

Exercise:
(1) Graph: f(x)= 2x+6;

(2) Graph: f(x)= -2x-8 , where -8 ≤ x < -1;

(3) Determine the linear function from the graph below.

(4) Two points (0, -8) and (10, 0) are known on a linear function, graph this linear function and determine the expression; If the function value is: -5 < f(x) ≤ 3, determine the range of x.

2. The slope of a linear function

chrisyang — 2016-10-26 11:00:19 UTC

The slope of a line is usually represented by the letter m. (x1, y1) represents the first point whereas (x2, y2) represents the second point. The slope is calculated by:

m=(y2−y1)/(x2−x1)

Exercise:
(1) Determine the slope of f(x) = -x + 5.

(2) Determine the slope of f(x) = 5.

(3) Determine the slope of f(x) =|x + 6|.

Draw Function Graphs

chrisyang — 2016-10-26 11:15:12 UTC

https://rechneronline.de/function-graphs/

GraphSketch.com

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Explore the Quadratic Equation

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https://www.mathsisfun.com/algebra/quadratic-equation-graph.html

3. Graphing quadratic functions

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Exercise:
(1) Graph: f(x) = 2x^2;
(2) Graph: f(x) = (1/2)x^2;
(3) Graph: f(x) = -x^2.

Larger values of a squash the curve inwards

Smaller values of a expand it outwards

And negative values of a flip it upside down

The End

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4. Graphing cubic functions

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Group discussion

5. More exercises

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Plot the graph below manually and in Excel.

5. More exercise answers in Excel

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Slides

chrisyang — 2016-10-27 09:34:29 UTC

3. Graphing quadratic functions

chrisyang — 2016-10-27 09:42:56 UTC

Self-learning, then graph the four exercises on the coordinate sheet and submit to this Padlet.

Coordinate Sheet

chrisyang — 2016-10-27 09:57:16 UTC