Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 (m) of a linear function represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you determine if a set of points represents a function?

Back

A set of points represents a function if each input (x-value) corresponds to exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

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

Given the function f(x) = -25x + 120, what is the output when x = 2?

Back

f(2) = -25(2) + 120 = 70.

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

If a plumber charges $25 for a house call and $120 per hour, what is the equation representing the total cost (C) for x hours?

Back

C = 120x + 25.

Front

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

Back

A table is a function if each input value (x) has a unique output value (y). No x-value should repeat with a different y-value.