Science:Math Exam Resources/Courses/MATH110/December 2017/Question 01 (a)
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Question 01 (a) 

Write down an algebraic expression (a formula) for a function whose domain is all and such that its graph goes through the point . 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

An example of function undefined at a single point is the reciprocal function. 
Hint 2 

Translate in both horizontal and vertical directions to meet the requirements. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. By Hint 1, we note that the function is defined for all real number .
By Hint 2, if we shift horizontally, we obtain a function which is defined for all real number .
Unfortunately, . In order that the graph of the function passes through , we translate vertically (using Hint 2 again) and consider This function is defined for all real number . Moreover, it satisfies as required.
Answer: The function can be . 