Functions and Linear Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input.

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does it mean for a mapping to be 'not a function'?

Back

A mapping is not a function if at least one input is associated with more than one output.

Front

How do you identify a function from a set of ordered pairs?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (x-value).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How do you write an equation for a linear function based on a real-world scenario?

Back

Identify the variables, determine the relationship, and express it in the form y = mx + b.

Front

What is the formula to calculate the total cost in a rental scenario?

Back

Total Cost (C) = Fixed Fee + (Hourly Rate × Number of Hours) or C = F + r*h.

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value).

Front

How do you find the slope from an equation in slope-intercept form?

Back

In the equation y = mx + b, the slope is the coefficient m.