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Given the description of the transformation from the function f to function g, write the function equation for g. graph the new function.
1. shift f(x) = cos(x) left pi units and up 5 units.
2. shift f(x) = sin(x) right pi/8 units and down pi units.
3. shift f(x) = cos(x) right 2pi/3 units and down 2pi units.
4. shift f(x) = sin(x) left 7/2 units and down 3 units.
5. shift f(x) = cos(x) right 4/5 units and up pi/6 units.
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To solve this problem and similar problems, you need to know THESE rules.
if you are given a function u = f(x) and its plot, then
- function v = f(x+a), where a > 0, has a plot shifted " a " units left comparing with u = f(x);
- function v = f(x-a), where a > 0, has a plot shifted " a " units right comparing with u = f(x);
- function v = f(x) + b, where b > 0, has a plot shifted " b " units up comparing with u = f(x);
- function v = f(x) - b, where b > 0, has a plot shifted " b " units down comparing with u = f(x).
THEREFORE, the requested (transformed/shifted) functions are
(1) y = cos(x + pi) + 5.
(2) y = sin(x - pi/8) - pi.
(3) y = cos(x - 2pi/3) -2pi.
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Now you have full instructions and three solved examples, which are your TEMPLATES.
Do the rest on your own.
You may post your answers to the forum for checking.
If you do, then PLEASE refer to the problem ID number 1174599 in order for the tutors would be able to identify the problem.
Happy learning (!)
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