4.8.2 Live Classroom

Front

What is a function?

Back

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

Front

How can you determine if a relation is a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the difference between continuous and discrete relations?

Back

Continuous relations can take any value within a range, while discrete relations consist of distinct, separate values.

Front

What is the vertex of an absolute value function?

Back

The vertex is the highest or lowest point of the graph, represented as (h, k) in the function f(x) = a| x - h| + k.

Front

How do you find the domain of a function?

Back

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

Front

What does the notation -5 < x < 7 mean?

Back

It means that x can take any value greater than -5 and less than 7.

Front

What is an absolute value function?

Back

An absolute value function is a function that contains an absolute value expression, typically in the form f(x) = a| x - h| + k.

Front

How does the 'a' value affect the graph of an absolute value function?

Back

The 'a' value determines the steepness and direction of the graph: if 'a' is positive, the graph opens upwards; if negative, it opens downwards.

Front

What is the significance of the coordinates (h, k) in an absolute value function?

Back

The coordinates (h, k) represent the vertex of the absolute value function, indicating the point where the graph changes direction.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, typically represented as (x, y) values.