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 f(x) = 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 value (y) changes for a unit change in the input value (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It is the value of f(x) when x = 0.

Front

How can you determine if a relation is a function?

Back

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

Front

What is the equation of a linear function with a slope of 2 and a y-intercept of 3?

Back

The equation is f(x) = 2x + 3.

Front

If f(x) = 5x - 4, what is f(2)?

Back

f(2) = 5(2) - 4 = 10 - 4 = 6.

Front

What are appropriate input values for the function Y = 40 + 10x?

Back

Appropriate input values are non-negative integers: 0, 1, 2, 3, ...

Front

What are appropriate output values for the function Y = 40 + 10x when x = 0, 1, 2?

Back

The output values are: Y(0) = 40, Y(1) = 50, Y(2) = 60.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input value (x) increases, the output value (f(x)) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input value (x) increases, the output value (f(x)) decreases.