Evaluating Linear Functions

Front

What is a linear function?

Back

A linear function is a function that can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

How do you evaluate a linear function at a given value of x?

Back

To evaluate a linear function at a given value of x, substitute the value of x into the function and simplify to find f(x).

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 f(x) changes for a unit change in x.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the value of f(x) when x = 0; it is the point where the line crosses the y-axis.

Front

Evaluate f(x) = 3x + 1 for x = 4.

Back

f(4) = 3(4) + 1 = 12 + 1 = 13.

Front

Evaluate f(x) = -2x + 5 for x = -1.

Back

f(-1) = -2(-1) + 5 = 2 + 5 = 7.

Front

What is the significance of the coefficient of x in a linear function?

Back

The coefficient of x in a linear function is the slope, which indicates the steepness and direction of the line.

Front

How can you determine if a function is linear from its equation?

Back

A function is linear if it can be written in the form f(x) = mx + b, where m and b are constants.

Front

Evaluate f(x) = 5x - 2 for x = 0.

Back

f(0) = 5(0) - 2 = 0 - 2 = -2.

Front

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

Back

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