word problem

Question

Please answer the following 3 questions:
1. What is a one-to-one function, and how can you determine if a given function is one-to-one? Provide complete details and answer in a complete sentence.

2. True or false (justify your decision): The graph of f(x) = (x + 2)³ + 6 is the graph of f(x) = x³ shifted 2 units right and 6 units up.

3. True or false (justify your decision): A rational function will always have a vertical asymptote.

Answer 1

1. A function is one-to-one if for any given x in your domain there exists an unique output in the range. In other words, you cannot have 2 x values being mapped to a single y value. 

 

2. False. Yes the graph is being moved 6 units up, but the (x+2)² is moving the graph to the left not the right. 

 

3. False. You will achieve a vertical asymptote (95% of the time) when the denominator of your rational function is zero. So, for example, if you had (x+3)/(x²+9) you would not have a vertical asymptote because the denominator is never 0.