Flashcard 3.2 Function Notation and Evaluating Functions (H)

Front

What is function notation?

Back

Function notation is a way to represent a function using symbols, typically written as f(x), where f is the name of the function and x is the input variable.

Front

How do you evaluate a function?

Back

To evaluate a function, substitute the given input value into the function's equation and simplify to find the output.

Front

Given g(x) = -8x + 1, evaluate g(-2).

Back

g(-2) = -8(-2) + 1 = 16 + 1 = 17.

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 (y-values) that the function can produce.

Front

Given f(x) = x^2 + 3, what input gives an output of 12?

Back

To find the input, set the equation: x^2 + 3 = 12. Solving gives x = 3 or x = -3.

Front

What does it mean if a function is increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What does it mean if a function is decreasing?

Back

A function is decreasing if, as the input values increase, the output values decrease.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, typically in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).