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

What does the slope of a linear function represent?

Back

The slope represents the rate of change of the function. It indicates how much the output (y-value) changes for a unit change in the input (x-value).

Front

What is the y-intercept of a linear function?

Back

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

Front

Evaluate f(0) if f(x) = 2x + 4.

Back

f(0) = 2(0) + 4 = 4.

Front

What is the definition of a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

Evaluate f(-5) if f(x) = -2x - 12.

Back

f(-5) = -2(-5) - 12 = 10 - 12 = -2.

Front

If f(x) = 6x - 9, what is 2f(12)?

Back

f(12) = 6(12) - 9 = 72 - 9 = 63, so 2f(12) = 2(63) = 126.

Front

Fill in the blank: If f(x) = 2x + 1, then f(___) = 13.

Back

f(6) = 2(6) + 1 = 12 + 1 = 13.

Front

What is the domain of a linear function?

Back

The domain of a linear function is all real numbers, as there are no restrictions on the input values.

Front

What is the range of a linear function?

Back

The range of a linear function is also all real numbers, as the output can take any value depending on the input.