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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