Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph, typically in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (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 y when x = 0 in the equation y = mx + b.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) is associated with exactly one output (y-value). This can be checked using the vertical line test on a graph.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean if a relation is 'not a function'?

Back

If a relation is 'not a function', it means that at least one input (x-value) is associated with more than one output (y-value).

Front

How do you find the total cost in a linear cost function?

Back

To find the total cost in a linear cost function, use the equation y = mx + b, where m is the variable cost per unit, x is the number of units, and b is the fixed cost.

Front

What is the significance of the coordinates in a relation?

Back

The coordinates in a relation represent pairs of input and output values, where the first value is the input (x) and the second value is the output (y).

Front

How do you write the equation of a linear function from a word problem?

Back

To write the equation of a linear function from a word problem, identify the fixed and variable costs, define the variables, and express the relationship in the form y = mx + b.