 # Construct Functions

Related Topics:
Common Core for Mathematics
More Math Lessons for Grade 8

Examples, solutions, videos, and lessons to help Grade 8 students learn how to construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Common Core: 8.F.4

### Suggested Learning Targets

• I can recognize that slope is determined by the constant rate of change
• I can recognize that the y-intercept is the initial value where x = 0
• I can determine the rate of change (slope) from two (x,y) values, a verbal description, values in a table, or graph.
• I can determine the initial value (y-intercept) from two (x,y) values, a verbal description, values in a table, or graph.
• I can construct a function to model a linear relationship between two quantities.
• I can relate the rate of change and initial value to real world quantities in a linear function in terms of the situation modeled and in terms of its graph or a table of values.
The following table shows how to construct linear functions from its graph or a table of values. Scroll down the page for more examples and solutions. Constructing Linear Functions (8.F.4)
Examples:
1. For your biRthday, you get \$100 gift card to a local bookstore. Each week, you treat yourself to a \$5 book. Write a function for the situation.
2. You own a bakery that makes muffins. The graph below represents the number of dozens of muffins you have (y), as a function of the number of hours since the bakery started work that day (x). Write a function for the situation.

Use Graphs and Tables to Represent Real World Situations and Solve Problems
Example:
The football booster club ordered 7,500 L of water for Friday night's game. The water sale averaged 150 L per minute. Solve the problem algebraically, numerically, and graphically to determine the amount of water remaining after 45 minutes? CCSS 8.F.4 - Modeling with Functions 8.F.4-1 - Constructing Linear Functions 8.f.4 Constructing a Linear Function
The Common Core State Standards (CCSS) videos are designed to support states, schools, and teachers in the implementation of the CCSS. Each video is an audiovisual resource that focuses on one or more specific standards and usually includes examples/illustrations geared to enhancing understanding. The intent of each content-focused video is to clarify the meaning of the individual standard rather than to be a guide on how to teach each standard although the examples can be adapted for instructional use. Conjecturing About Functions
Grades 6-8 / Math / Reasoning
CCSS: Math.8.F.B.4 Math.Practice.MP2 Math.Practice.MP3
Lesson Objective
Analyze patterns and represent functions.

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