 ## Let's Get Started

We are going to learn how to determine the reasonableness of the domain and range of quadratic functions when given a real-world example.

TEKS Standards and Student Expectations

A(1) Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:

A(1)(B) use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution

A(1)(G) display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication

A(6) Quadratic functions and equations. The student applies the mathematical process standards when using properties of quadratic functions to write and represent in multiple ways, with and without technology, quadratic equations. The student is expected to:

A(6)(A) determine the domain and range of quadratic functions and represent the domain and range using inequalities

Resource Objective(s)

Determine restrictions on the domain and range of the function when given a situation that can be modeled by a quadratic function or its graph.

Essential Questions

What makes a domain or range reasonable?

How do you know when the domain or range of a function should have restrictions?

Vocabulary

## Is it Reasonable?

How to Determine the Restricted Domain and Range of a Quadratic Function

If the domain and range of a quadratic function are not reasonable when given a problem situation, then the function may have restrictions. Follow the four steps below as a guide for determining the restricted domain and range of a quadratic function in a real-world example. Click on each step to see an algorithm to check for restrictions.

Example: The Bird’s Nest Problem A bird is building a nest in a tree that is 36 feet above the ground. The bird dropped a stick from the nest. The function f(x) = -16x2 + 36 describes the height of the stick in feet after x seconds. Using the steps you have learned and the accompanying chart, identify the domain and range of the function.

## Reasonableness of Domain and Range—Video

View the video below on reasonable domain and range. You will be prompted by the video instructor to pause the video and complete practice problems. Complete the problems as instructed and then press play to view the answers.