New Zealand
Level 8 - NCEA Level 3

# Identify Characteristics of Rational Functions

## Interactive practice questions

Finding solutions to rational equations requires careful consideration. Fill in the missing number:

"A proposed solution of a rational equation must be rejected if it causes a denominator to equal $\editable{}$."

Easy
Less than a minute

What is the resulting equation after we clear the fractions? Do not solve the equation.

 $\frac{8}{\left(x+6\right)\left(x-6\right)}$8(x+6)(x−6)​ $=$= $\frac{5}{x-6}+\frac{4}{x+6}$5x−6​+4x+6​ $\left(x+6\right)\left(x-6\right)\times\frac{8}{\left(x+6\right)\left(x-6\right)}$(x+6)(x−6)×8(x+6)(x−6)​ $=$= $\left(x+6\right)\left(x-6\right)\left(\frac{5}{x-6}+\frac{4}{x+6}\right)$(x+6)(x−6)(5x−6​+4x+6​)

A rational equation can have no solution. True or false?

Consider the following graph of a hyperbola.

### Outcomes

#### M8-7

Form and use trigonometric, polynomial, and other non-linear equations

#### 91575

Apply trigonometric methods in solving problems