Function Notation

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

What is the dependent variable in a function?

Back

The dependent variable is the output of a function, which depends on the input variable. For example, in the function f(x) = 2x + 1, the output (f(x)) depends on the value of x.

Front

What does f(2) mean in function notation?

Back

f(2) means to evaluate the function f at the input value of 2, essentially substituting 2 for x in the function.

Front

How do you determine if a mapping is a function?

Back

A mapping is a function if each input value is associated with exactly one output value.

Front

What is the first step to evaluate f(1) for f(x) = 2x + 1?

Back

The first step is to plug a 1 in for all the x's in the function.

Front

What is the output of the function f(x) = -3x + 3 when x = 0?

Back

The output is 3, since f(0) = -3(0) + 3 = 3.

Front

What does it mean for a function to be linear?

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 in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function; it indicates how much the output (y) changes for a unit change in the input (x).

Front

What is the y-intercept in a linear function?

Back

The y-intercept (b) is the value of the function when the input (x) is 0; it is the point where the graph intersects the y-axis.

Front

How do you find the output of a function for a given input?

Back

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