Linear Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 represents the rate of change of the function, indicating 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, represented by the value of b in the equation f(x) = mx + b.

Front

If f(x) = 2x + 3, what is f(5)?

Back

f(5) = 2(5) + 3 = 10 + 3 = 13.

Front

What is the difference between input and output in a function?

Back

Input is the value you provide to the function (x), while output is the value the function returns (f(x)).

Front

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

Back

A relation is a function if each input value corresponds to exactly one output value.

Front

If the slope of a line is 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning the output value does not change regardless of the input value.

Front

What is the formula for calculating the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

In the equation Y = 40 + 10x, what does the 40 represent?

Back

The 40 represents the initial value or the y-intercept, which is the cost before any monthly fees are added.

Front

What is the output when the input is 0 in the function Y = 40 + 10x?

Back

When the input is 0, the output is Y = 40 + 10(0) = 40.