In this worksheet, we will practice identifying reciprocal functions and their properties and identifying asymptotes, domains, and ranges.
Consider the function .
By considering the point at which the denominator equals zero, find the domain of the function.
To find the range of the function, a handy trick is to divide the numerator and denominator of through by . What expression does this give us?
Now, taking the limit of this expression as tends to infinity will give us the value of which is not in the range of the original function. Use this to state the range of the function.
Hence, state the equations of the two asymptotes.
- A and
- B and
- C and
- D and
- E and
The following is the graph of the triangle wave function .
What is the domain of its reciprocal function ?
- Aeven integers
- Ball real numbers
- Codd integers
- Dall real numbers that are not integers
- Eall integers