1)Transformations of the form f (x) + c?
(a) In Maple, create a text region and enter the following sentence: Translations of the form f(x) + c. Insert an execution group (command prompt) after the the text region.
(b) In Maple, create the function f (x) =|x
(c) Plot f (x) in the colour blue, with both the x-axis and the y-axis varying from -10 to 10.
(d) Plot f (x) in the colour blue together with f (x) + 3 in the colour red and f (x) - 2 in the colour green. On the printout of this worksheet, label each function by writing the name of the function by each graph.
(e) QUESTION: How does adding a positive constant to a function affect it?
(f ) QUESTION: How does subtracting a positive constant from a function affect it?
2). Transformations of the form f (x + c).
(a) In Maple, create a text region and enter the following sentence: Translations of the form f(x + c). Insert an execution group (command prompt) after the the text region.
(b) In Maple, create the function f (x) = x3 .
(c) Plot f (x) in the colour blue, with both the x-axis and the y-axis varying from -10 to 10.
(d) Plot f (x) in the colour blue together with f (x + 5) in the colour red and f (x - 3) in the color green. On the
printout of this worksheet, label each function.
(e) QUESTION: How does adding a positive constant to the x-component of a function affect it?
(f ) QUESTION: How does subtracting a positive constant from the x-component of a function affect it?
(g) In Maple, plot f (x) in the colour blue together with f (x + 2) - 1 in the colour brown. This is a combined
QUESTION: Describe what this combination of translations does to the function?
3)Transformations of the form f (-x) and -f (x).
(a) In Maple, create a text region and enter the following sentence: Reflections of f(x). Insert an execution group(command prompt) after the the text region.(b) In Maple, create the function f (x) = 3x. (HINT: use f := x -> 3?x;) (c) Plot f (x) in the colour blue, with the x-axis varying from -5 to 5.
(d) Plot f (x) in the colour blue together with -f(x) in the colour red and f (-x) in the color green. On the printout
of this worksheet, use a pencil to label
each function
(e) QUESTION: How does multiplying by -1 affect a function?
(f ) QUESTION: How does multiplying the x-component of a function by -1 affect it?
4a) In Maple, create a text region and enter the following sentence: Stretching and Compressing f(x). Insert an execution group (command prompt) after the the text region.(b) In Maple, create the function f (x) = cos x. (HINT: use f := x -> cos(x);) (c) Plot f (x) in the colour blue, with the x-axis varying from -5 to 5.
(d) Plot f (x) in the colour blue together with 2f (x) in the colour red and f ((1/2) x) in the color green. On the printout of this worksheet, label each function.
NOTE: remember to use an * for
multiplication in Maple.
(e) QUESTION: How does multiplying by 2 affect the function?>
(f ) QUESTION: How does multiplying the x-component by 1 affect the function?
5)In Maple, plot the graph of f (x) = x2 in the colour blue together with the function g(x) = 2x in the colour red. Use the x-axis range of your choice-you may have to try adjusting your x-axis range a few times to get an accurate picture. QUESTION: Which function grows more quickly when x is large? How can you tell from the graphs?
6. Plot the following functions on the same set of axis. You can use the x-axis range and colours of your choice: f (x) = 2^x, g(x) = 5^x, h(x) = 20^x and k(x) = e^x. (HINT: Recall in Maple that e^x is exp(x). Label the functions on your printout. QUESTION: For large x, which function grows more quickly?
6b)Write the MAPLE EXPRESSIONS AND MATHEMATICAL EXPRESSIONS FOR f(x)=e^x when 1)=SHIFTS 2 TO THE RIGHT? 2)When reflects about x-axis? 3)When reflects about y-axis? 4)When it shifts upward by 2 and reflects about Y-axis? 5)REFLECTS ABOUT X-AXIS AND REFLECTS ABOUT Y-AXIS?
c) Determine a vector equation of the line of intersection of the planes
2x1 - x2 - 2x3 = 7 and x1 + 5x2 + 3x3 = -2.?
6d) Determine by a projection the point on the hyperplane
x1 + 2x2 + 2x3 + x4 = 6 that is closest to the point Q(2,3, 2,-1)