Evaluate Functions

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does f(x) represent in a function?

Back

f(x) represents the output of the function f for a given input x.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the input into the function's equation.

Front

What is the function f(x) = 3x - 8 evaluated at x = 6?

Back

f(6) = 3(6) - 8 = 18 - 8 = 10.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (f(x) values) that the function can produce.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form f(x) = mx + b.

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 f(x) when x = 0; it is the point where the graph intersects the y-axis.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

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