The Student Will Evaluate and Plot Functions

The Student Will Evaluate and Plot Functions

Plotting functions

Evaluation Table
y = x + 3
x / y / Point
0
1
2
3
4
5
6
7
8
9
10 / 3
4
5
6
7
8
9
10
11
12
13 / (0,3)
(1,4)
(2,5)
(3,6)
(4,7)
(5,8)
(6,9)
(7,10)
(8,11)
(9,12)
(10,13)

Objective

The student will evaluate and plot functions.

Materials

Pencil, paper, colored pencils, graph paper, ruler

Instructions

  1. For each of the following formulas and ranges, create evaluation tables similar to the example.
    Set 1: Positive slope
    Formulax range
    y = x + 30 to 10
    y = x + 50 to 10
    y = 2x0 to 10
    y = 2x + 30 to 10
  2. Create an XY coordinate grid large enough to encompass all of the points in the evaluation tables.
  3. Plot the points of each function and connect with a straight line. Draw each line with a different line scheme (pattern or color).
  4. Create a legend indicating each function’s line scheme.

Grading

You will be graded on the following criteria:

NeatnessReadability of the evaluation tables, XY coordinate grid, and function plots.

AccuracyCorrectly evaluating and plotting the functions.

Additional Function Sets

Set 2: Positive and negative slope

Formulax range
y = x0 to 15
y = x + 50 to 15
y = 5 – x0 to 5
y = 10 – x0 to 10
y = x – 55 to 15 /

Set 3: Varying positive slope

Formulax range
y = x/100 to 10
y = x/50 to 10
y = x/40 to 10
y = x/30 to 10
y = x/20 to 10
y = x0 to 10
y = 2x0 to 10
y = 3x0 to 10
y = 4x0 to 10
y = 5x0 to 10
y = 10x0 to 10 /

Set 4: Picture design

Formulax range
y = x0 to 24
y = 2x0 to 8
y = 2x - 2416 to 24
y = x/20 to 16
y = x/2 + 128 to 24
y = 3x0 to 6
y = 3x – 4818 to 24
y = x/30 to 18
y = x/3 + 166 to 24
y = 24 – x6 to 18

Activity 2 – Parabolas

y = x2
x / y
-5
-4
-3
-2
-1
0
1
2
3
4
5 / 25
16
9
4
1
0
1
4
9
16
25

Objective

The student will plot parabolas on an XY coordinate system.

Topics

Coordinate systemEvaluating functionsGeometric patternsPlotting points

Negative integersDecimalsExponentsParabolas

Materials

Pencil, graph paper, colored pencils, ruler, calculator

Instructions

  1. Create the XY coordinate grid to the right on graph paper.
  2. For each of the following formulas, create evaluation tables similar to the example. X should range from –5 to 5 for all tables.
    y = x2y = x2 – 1
    y = x2 + 2 y = x2 – 2
    y = x2 + 5 y = x2 – 5
    y = x2 + 10 y = x2 – 10
  3. Plot the points of each function and connect with a parabola. Do not plot any points outside of the grid area. Color each parabola with a different color.
  4. Create a legend indicating each function’s color.

Extra Credit:

Complete the above instructions for x values from –7 to 7, and y values from –5 to 50.

Grading

You will be graded on the following criteria:

NeatnessReadability of the evaluation tables, XY coordinate grid, and function plots.

AccuracyCorrectly evaluating and plotting the functions.

Activity 3 – Parabolas II

Objective

y = 5x2
x / y
-5
-4
-3
-2
-1
0
1
2
3
4
5 / 125
80
45
20
5
0
5
20
45
80
125

The student will evaluate and plot a set of second degree functions to create a picture.

Instructions

  1. Create the following XY Coordinate Grid system:
    x-range:-10 to 10
    y-range:-5 to 30
  2. For each of the following formulas and ranges, create evaluation tables similar to the example.
    Formulax rangeFormulax range
    y = x2-5 to 5
    y = 2x2-5 to 5y = x2 2-10 to 10
    y = 3x2-5 to 5y = x2 3-10 to 10
    y = 4x2-5 to 5y = x2 4-10 to 10
    y = 5x2-5 to 5y = x2 5-10 to 10
  3. Plot the points of each function and connect with a smooth line. Do not plot points that fall outside of the specified grid area. Color each line with a different color.
  4. Create a legend indicating each function’s color.

Grading

You will be graded on the following criteria:

NeatnessReadability of the evaluation tables, XY coordinate grid, and function plots.

AccuracyCorrectly evaluating and plotting the functions.

Activity 4 – Parabolas III

Objective

The student will evaluate and plot a set of second degree functions to create a picture.

Instructions

  1. Create the following XY Coordinate Grid system:
    x-range:-5 to 5
    y-range:-15 to 20
  2. For each of the following formulas and ranges, create evaluation tables similar to the example.
    Formulax range
    y = 20 – x2-5 to 5
    y = 10 – x2 -5 to 5
    y = 5 – x2-5 to 5
    y = – x2-5 to 5
    y = -5 – x2-5 to 5
  3. Plot the points of each function and connect with a smooth line. Do not plot points that fall outside of the specified grid area. Color each line with a different color.
  4. Create a legend indicating each function’s color.

Grading

You will be graded on the following criteria:

NeatnessReadability of the evaluation tables, XY coordinate grid, and function plots.

AccuracyCorrectly evaluating and plotting the functions.

Activity 5 – Parabolas IV

Objective

Formula / x range
/ -10 to 10
/ -10 to 10
/ -10 to 10
/ -10 to 10
/ -10 to 10

The student will evaluate and plot a set of second degree functions to create a picture.

Instructions

  1. Create the following XY Coordinate Grid system:
    x-range:-10 to 10
    y-range:-20 to 15
  2. For each of the formulas and ranges, create evaluation tables.
  3. Plot the points of each function and connect with a smooth line. Do not plot points that fall outside of the specified grid area. Color each line with a different color.
  4. Create a legend indicating each function’s color.

Extra Credit

Include the following formulas in your document:

Grading

You will be graded on the following criteria:

NeatnessReadability of the evaluation tables, XY coordinate grid, and function plots.

AccuracyCorrectly evaluating and plotting the functions.

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