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In this lesson, we will learn how to identify reciprocal functions and their properties and how to identify asymptotes, domains, and ranges.
Q1:
The figure shows the graph of π¦ = 1 π₯ .
Write down the equations of the two asymptotes of π¦ = 1 π₯ .
What is the domain of the function?
What is the range of the function?
Q2:
The following is the graph of the triangle wave function π¦ = π ( π₯ ) .
What is the domain of its reciprocal function π ( π₯ ) = 1 π ( π₯ ) ?
Q3:
Consider the function π¦ = 3 π₯ 5 π₯ + 7 .
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 3 π₯ π₯ + 7 through by π₯ . What expression does this give us?
Now, taking the limit of this expression as π₯ tends to infinity will give us the value of π¦ 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.
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