Qualitative Graphs

Front

What is a qualitative graph?

Back

A qualitative graph is a visual representation that shows the relationship between two variables without using numerical values, focusing on the general shape and trends of the data.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be represented by a straight line on a graph, indicating a constant rate of change between the variables.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input (x) values increase, the output (y) values also increase.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing if, as the input (x) values increase, the output (y) values decrease.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, indicating that the rate of change varies.

Front

How can you identify a linear function on a graph?

Back

A linear function can be identified by a straight line, where the slope remains constant throughout.

Front

What is the significance of the slope in a linear graph?

Back

The slope indicates the rate of change of the dependent variable (y) with respect to the independent variable (x). A positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

What does it mean for a graph to be 'decreasing and nonlinear'?

Back

It means that as the x-values increase, the y-values decrease, and the graph does not form a straight line.

Front

What is the importance of identifying key points on a graph?

Back

Identifying key points, such as maximums, minimums, and points of inflection, helps in understanding the behavior of the function.

Front

What is a vertex in the context of a graph?

Back

A vertex is a point where the graph changes direction, such as the highest or lowest point on a curve.