Key Features of Graphs

Front

What are the x-intercept(s) of a graph?

Back

The x-intercept(s) are the points where the graph intersects the x-axis, represented as (x, 0). For example, (0, 0) and (4, 0) are x-intercepts.

Front

How do you identify the maximum and minimum points of a function on a graph?

Back

The maximum point is the highest point on the graph, while the minimum point is the lowest point. For example, maximum (-5, 25) and minimum (15, -15).

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph intersects the y-axis, represented as (0, y). For example, (0, 7) is a y-intercept.

Front

What does it mean for a graph to be continuous?

Back

A continuous graph means that there are no breaks, holes, or gaps in the graph; it can be drawn without lifting the pencil.

Front

How do you determine the minimum value of a graph?

Back

The minimum value is the lowest point on the graph. For example, the minimum of this graph is (-0.5, -3.5).

Front

What is the significance of the x-axis in a graph?

Back

The x-axis is the horizontal line on a graph that represents the independent variable, typically denoted as 'x'.

Front

What is the significance of the y-axis in a graph?

Back

The y-axis is the vertical line on a graph that represents the dependent variable, typically denoted as 'y'.

Front

What is a vertex in the context of a graph?

Back

A vertex is a point where two or more curves, lines, or edges meet. In a parabola, the vertex is the maximum or minimum point.

Front

What is the difference between a local maximum and a global maximum?

Back

A local maximum is the highest point in a specific interval, while a global maximum is the highest point over the entire graph.

Front

How can you find the intercepts of a graph algebraically?

Back

To find the x-intercepts, set y=0 and solve for x. To find the y-intercept, set x=0 and solve for y.