Describing Graphs

Front

What is a graph in mathematics?

Back

A graph is a visual representation of data that shows the relationship between two or more variables, typically using a coordinate system.

Front

Define the x-axis and y-axis in a Cartesian plane.

Back

The x-axis is the horizontal line in a Cartesian coordinate system, while the y-axis is the vertical line. Together, they form the axes for plotting points.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate, indicating how steep the line is.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is zero.

Front

Explain the concept of a function in relation to graphs.

Back

A function is a relation where each input (x-value) has exactly one output (y-value). In a graph, this means that a vertical line drawn anywhere on the graph intersects the curve at most once.

Front

What is a quadratic function and how is it represented graphically?

Back

A quadratic function is a polynomial function of degree 2, typically represented as f(x) = ax^2 + bx + c. Its graph is a parabola.

Front

What does it mean for a graph to be increasing or decreasing?

Back

A graph is increasing when the y-values rise as the x-values increase, and decreasing when the y-values fall as the x-values increase.

Front

Define the term 'asymptote' in graphing.

Back

An asymptote is a line that a graph approaches but never touches, indicating the behavior of the graph as it extends towards infinity.

Front

What is the difference between a continuous and a discrete graph?

Back

A continuous graph has no breaks and can be drawn without lifting the pencil, while a discrete graph consists of distinct points that are not connected.