Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

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.

Donβt have an account? Sign Up