Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

What are the domain restrictions for the middle piece of the function defined as f(x) = { x^2 for x < 1, 2x + 1 for 1 ≤ x < 3, -x + 5 for x ≥ 3 }?

Back

1 ≤ x < 3

Front

How do you find the value of a piecewise function at a specific point, for example, h(5)?

Back

Evaluate the function using the expression that corresponds to the domain where x = 5.

Front

What is the output of h(5) if h(x) = { -x^2 for x < 1, 2x + 1 for 1 ≤ x < 3, -x + 5 for x ≥ 3 }?

Back

7

Front

What is the general form of a piecewise function?

Back

f(x) = { expression1 for condition1, expression2 for condition2, ... }

Front

What does it mean if a piecewise function is undefined at a certain point?

Back

It means that there is no expression defined for that specific input value in the function.

Front

How can you determine the correlation type from a graph?

Back

By observing the direction of the trend: upward indicates positive correlation, downward indicates negative correlation, and no trend indicates no correlation.

Front

What type of correlation is shown if the graph slopes downward?

Back

Negative correlation.

Front

What type of correlation is shown if the graph has no visible trend?

Back

No correlation.

Front

What is the significance of domain restrictions in piecewise functions?

Back

Domain restrictions define the intervals over which each piece of the function is applicable.