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.

Tags

CCSS.5.G.A.1

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.

Tags

CCSS.8.EE.B.5

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).

Tags

CCSS.8.EE.B.5

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7A

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.

Tags

CCSS.HSF-IF.C.7D

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5