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 and b are constants, and m is the slope of the line.

Front

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

Back

To evaluate a linear function at a specific value of x, substitute the value of x into the function and simplify the expression.

Front

What does the slope (m) represent in a linear function?

Back

The slope (m) represents the rate of change of the function; it indicates how much the output (f(x)) changes for a unit change in the input (x).

Front

What does the y-intercept (b) represent in a linear function?

Back

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

Front

Evaluate f(x) = -x for x = 10.

Back

f(10) = -10.

Front

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

Back

f(-2) = -9.

Front

Evaluate f(x) = -4x + 2 for x = 1.

Back

f(1) = -2.

Front

Evaluate f(x) = 2x for x = 3.

Back

f(3) = 6.

Front

Evaluate f(x) = x - 7 for x = 5.

Back

f(5) = -2.

Front

What is the general form of a linear function?

Back

The general form of a linear function is f(x) = mx + b.