In this lesson, we will learn how to identify, write, and evaluate a rational function.
Q1:
The figure shows the graph of 𝑦=1𝑥.
Write down the equations of the two asymptotes of 𝑦=1𝑥.
What is the domain of the function?
What is the range of the function?
Q2:
Consider the function 𝑦=3𝑥5𝑥+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 3𝑥5𝑥+7 through by 𝑥. What expression does this give us?
Now, taking the limit of this expression as 𝑥 tends to infinity will give us the value of 𝑦 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.
Q3:
The following is the graph of the triangle wave function 𝑦=𝑔(𝑥).
What is the domain of its reciprocal function 𝑓(𝑥)=1𝑔(𝑥)?
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