Science:Math Exam Resources/Courses/MATH110/December 2012/Question 01 (a)
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Question 01 (a) 

Sketch the graph of the following function.

Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

What does a normal cosine graph look like? Look at what happens to some test values like or if you plug them into the function given above instead of a normal cosine function. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The graph of looks like this: The rules for shifting functions tell us that
giving: 
Solution 2  

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. If you've forgotten the rules used in the first solution (or never learned them), you can also use test points. From this picture: you have the following points, placed in a table of values:
Plugging these same xvalues into gives:
Drawing a picture based on these points, it should be clear that the graph has been shifted right by and expanded vertically by 2. 