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

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 

Recall that for the usual logarithm, , x can't be zero or negative. Which values of x will make sure that the above function doesn't end up with a negative or zero value inside the logarithm? 
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: Using function rules for the graph of
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 facts about the domain of to determine where the graph should go. The domain of the function is which can be seen in the graph below. The graph of will have a similar shape, but has a different domain. Let's test some values to see where the domain of this function is.
So clearly this function is defined on the domain , suggesting the graph looks something like this: 