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

Front

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

Back

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

Front

Evaluate f(x) = 2x + 3 for x = 4.

Back

f(4) = 2(4) + 3 = 8 + 3 = 11.

Front

Evaluate f(x) = -3x + 6 for x = 2.

Back

f(2) = -3(2) + 6 = -6 + 6 = 0.

Front

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

Back

f(1) = 5(1) - 1 = 5 - 1 = 4.

Front

Evaluate f(x) = 0.5x + 2 for x = 8.

Back

f(8) = 0.5(8) + 2 = 4 + 2 = 6.

Front

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

Back

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

Front

What is the significance of a negative slope in a linear function?

Back

A negative slope indicates that as x increases, f(x) decreases, showing an inverse relationship between x and f(x).