FUN with FUNctions PROJECT
In addition to writing a test on Transformations of Functions, you are to create a picture using the functions you have studied. (Linear, Constant, Quadratic, Cubic, Reciprocal, Absolute Value, Exponential, Square Root.) You may include relations which are not functions such vertical lines (x = k) and circles (x2 + y2 = r2). Your creation must include at least 5 different functions. You may use a function more than once. Using the same function 5 times is not using 5 different functions.
In the computer lab:
Log on. Hit Start. Go to All programs. Graph, then graph again.
Go to “Function”
Type in the function next to f(x)
Note: All equations must be rewritten as functions of x. That is, you have to isolate y in order to enter the function.
To modify function, select by double clicking on the function to be modified at the left hand side of the screen and make any changes. Changes can include making it thicker, changing the colour, etc. Colour will not show up when you print using the school printer.
Note: To show the list of all functions used, choose landscape when printing.
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WARM UP
You may wish to start by graphing the following examples to get a feel for how the program works and what the functions look like!
Line:
y = x x slope = 1 and y-int = 0
y = x + 2 x + 2 slope = 1 and y-int = 2
y = 2x 2x slope = 2 and y-int = 0
y = 3 3 horizontal line at y = 3
To restrict the domain, enter minimum and maximum x values into the “argument range” box.
Parabola: What to type in
y = x2 x^2
y = (x-2)2 + 1 (x-2) ^ 2 + 1 shift 2 right and 1 up
y = 2x2 2x^2 vertical expansion of a factor of 2
y = -x2 -x^2 reflection on the x-axis
Absolute value:
y = |x| abs x
y = |x-2| + 1 abs (x-2) + 1 shift 2 right and 1 up
y = 2|x| 2 abs x vertical expansion of a factor of 2
y = -|x| -abs x reflection on the x-axis
Cubic function:
y = x3 x^3
y = (x-2)3 + 1 (x-2) ^ 3 + 1 shift 2 right and 1 up
y = 2x3 2x^3 vertical expansion of a factor of 2
y = -x3 -x^3 reflection on the x-axis
Exponential Function:
y = 2x 2^x
y = -2x -2^x reflection in the x-axis
y = 2–x 2^(-x) refelction in the y-axis
Square root function:
y = √ x sqrt x
y = √(x-2) + 1 sqrt (x-2) + 1 shift 2 right and 1 up
y = 2√x 2 sqrt x vertical expansion of a factor of 2
y = -√x -sqrt x reflection on the x-axis
y = √-x sqrt -x reflection on the y-axis
Reciprocal function:
y = 1/x 1/x
y = 1/x + 2 1/x + 2 shifts up 2
y = 1/(x+2) 1/(x+2) shifts left 2
y = 1/(x-3) +5 1/(x-3) + 5 shifts right 3 and up 5
Circle:
Note: a circle is not a function. But the top ½ only is. Also, just the bottom ½ alone is.
x2 + y2 = 9 This is a circle with a radius of 3 with its centre at (0,0)
Need to isolate the y
y = √(9 – x2) sqrt (9 – x^2) top ½ , radius 3, centre (0,0)
y = -√(9 – x2) -sqrt (9 – x^2) bottom ½ , radius 3, centre (0,0)
y = √(9 – (x-2)2) +1 sqrt (9 – (x-2)^2) +1 top ½ , radius 3, centre (2,1)
y = -√(9 – (x-2)2) -sqrt (9 – (x-2)^2)+1 bottom ½ , radius 3, centre (2,1)
to make a bigger circle change the radius
y = √(25 – x2) sqrt (25 – x^2) top ½ , radius 5, centre (0,0)
to make a stretched circle (like an egg) put a # in front (vertical expansion)
y = 2√(9 – x2) 2sqrt (9 – x^2) top ½ , 3 wide, 6 tall, centre (0,0)
Sine wave
y = sin x sin x
To restrict the domain use the argument range function
y = sin x + 1 sin x + 1 shift 1 up
y = 2sin x 2 sin x vertical expansion of a factor of 2
Reminder! A vertical line is NOT a function. However, you may wish to include vertical lines in your picture.
Vertical lines:
For vertical lines use insert point series, found under functions.
Note: point series is only allowed for vertical lines, use functions for all other lines.
Choose the x and y value of 2 pts. The x values should be the same for both pts.
X Y
3 -5
3 2
This creates 2 dots, one at (3,-5) and one at (3, 2).
Change shape and size of dots using Style and Size under Marker.
Connect the dots by changing Style under Line.
This creates a vertical line at x = 3 that is 7 units long, starting at -5 and goes to 2
To make the dots disappear, change dot size to zero.
Have FUN with FUNctions!