Graded CW #3 - Comparing Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for two functions to be compared?

Back

Comparing two functions involves determining which function has a greater value at a specific input or identifying where one function is greater than the other.

Front

What is the notation for a function?

Back

The notation f(x) represents the value of the function f at the input x.

Front

How do you determine f(2) from a graph?

Back

To find f(2), locate the point on the graph of f where x = 2 and read the corresponding y-value.

Front

What does it mean if f(x) < g(x)?

Back

It means that the value of function f at x is less than the value of function g at the same x.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input to the function, and it determines the corresponding output value.

Front

How can you tell if two functions are equal at a certain point?

Back

Two functions are equal at a point if their outputs are the same for that input, i.e., f(x) = g(x).

Front

What is the graphical representation of a function?

Back

A function can be represented graphically as a curve or line on a coordinate plane, where the x-axis represents inputs and the y-axis represents outputs.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input x increases, the output f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input x increases, the output f(x) decreases.