Pre-Algebra 7: Chapter 7 Functions

Questions and Answers

What type of data involves a count of items?

Linear function

Continuous data

Discrete data (correct)

Function

What is continuous data?

Continuous data are data where numbers between any two data values have meaning.

Define a function.

A function is a rule that assigns to each input value exactly one output value.

What is a function rule?

A function rule is an equation that describes a function. Signup and view all the answers

When is an equation considered a linear equation?

If it forms a straight line when graphed Signup and view all the answers

What defines a linear function?

A linear function is a function whose points lie on a straight line when the function is graphed. Signup and view all the answers

If data does not form a straight line when graphed, then its change is nonlinear.

True Signup and view all the answers

What is a proportional relationship?

A proportional relationship is a relationship between inputs and outputs in which the ratio of inputs and outputs is always the same. Signup and view all the answers

What is slope?

Slope is a ratio that describes steepness, calculated as Slope = vertical change/horizontal change = rise/run. Signup and view all the answers

What is the formula for the slope of a line?

Slope = change in y coordinates/change in x coordinates = rise/run. Signup and view all the answers

What is slope-intercept form?

An equation written in the form y = mx + b is in slope-intercept form. Signup and view all the answers

What is a y-intercept?

The y-intercept is the point where the graph of a function crosses the y-axis. Signup and view all the answers

Study Notes

Data Types

Continuous data: Values between any two data points are meaningful; represented by a solid line.
Discrete data: Involves counting items (e.g., people, cars); depicted with plotted points connected by a dashed line.

Functions

Function: A rule mapping each input to exactly one output.
Function rule: An equation that represents a specific function.

Linear Equations and Functions

Linear equation: Creates a straight line when graphed.
Linear function: Points on the graph of a linear function lie in a straight line.

Nonlinear Relationships

Nonlinear: Data that does not form a straight line when graphed indicates a nonlinear relationship.

Relationships and Ratios

Proportional relationship: Maintains a constant ratio between inputs and outputs.

Slope

Slope: A measure of steepness calculated as the vertical change divided by the horizontal change (rise/run).
Slope of a line: Formula involves change in y coordinates over change in x coordinates, simplified to rise/run.

Slope-Intercept Form

Slope-intercept form: An equation of the form y = mx + b, where m represents the slope and b the y-intercept; results in a linear graph.
Y-intercept: The point at which a graph intersects the y-axis.

Description

Explore the concepts of continuous and discrete data in Pre-Algebra 7. This quiz will help you understand the fundamental differences between these types of data and how to represent them visually. Perfect for mastering Chapter 7 on functions!