# Let's Get Started

Let's practice writing verbal descriptions of functional relationships.

**TEKS Standards and Student Expectations**

**A(2)** Linear functions, equations, and inequalities. The student applies the mathematical process standards when using properties of linear functions to write and represent in multiple ways, with and without technology, linear equations, inequalities, and systems of equations. The student is expected to:

**A(2)(C)** write linear equations in two variables given a table of values, a graph, and a verbal description

**A(4)** Linear functions, equations, and inequalities. The student applies the mathematical process standards to formulate statistical relationships and evaluate their reasonableness based on real-world data. The student is expected to:

**A(4)(C)** write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

**A(8) **Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data. The student is expected to:

**A(8)(B) **write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

**Resource Objective(s)**

Verbally describe the functional relationship that exists when given a problem situation.

**Essential Questions**

How can you tell if a situation is linear or quadratic?

Why is it important to mention if there are any restrictions with the independent variable when writing a verbal description?

**Vocabulary**

- Function
- Linear Function
- Quadratic Function
- Constant
- Independent Variable
- Dependent Variable

# Describing a Linear Function

In math, verbal representations of the functions describing a problem situation are sometimes used instead of an equation.

**Example 1**

Maria just purchased a new compact car, hoping to save money driving to work and back. Maria tracked her expenses for six months in order to determine the average monthly cost of operating her new car. In addition to the cost of gas ($4 per gallon), Maria calculated a monthly fee of $120, which includes maintenance and insurance costs.

This is a graph of the function of Maria's monthly car cost. Press the animate button to move the car along the horizontal axis and view the graph. Then answer the following question to check your understanding.

Press the animate button to move the car along the horizontal axis below to view another graph of Maria's cost to drive her car. Then think about the questions that follow.

# Including Restrictions in the Description of the Function

Jose is creating patterns with square bricks in his backyard to highlight his garden. Click through the slideshow below to view the next pattern and then continue clicking to view the progression.

# Review of Writing a Description of a Problem Situation

Watch the following Prezi showing the information needed when writing a complete description of a problem situation.