Evaluating 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

How do you evaluate a linear function?

Back

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

Front

What is the slope in a linear function?

Back

The slope (m) in 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 does the y-intercept represent in a linear function?

Back

The y-intercept (b) is the value of f(x) when x = 0. It represents 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 = 11.

Front

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

Back

f(3) = 2(3) = 6.

Front

Evaluate f(x) = -x + 3 for x = 3.

Back

f(3) = -3 + 3 = 0.

Front

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

Back

f(10) = -10.

Front

Evaluate f(x) = -10x + 2 for x = 5.

Back

f(5) = -10(5) + 2 = -50 + 2 = -48.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as you can input any real number for x.