Interpreting Graphs of Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as a set of ordered pairs, a graph, or an equation.

Front

What does the slope of a graph represent?

Back

The slope of a graph represents the rate of change of the dependent variable with respect to the independent variable. It indicates how steep the graph is.

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the graph intersects the y-axis. It represents the value of the dependent variable when the independent variable is zero.

Front

How can you determine if a graph is increasing or decreasing?

Back

A graph is increasing if it moves upward from left to right, and decreasing if it moves downward from left to right.

Front

What does a horizontal line on a graph indicate?

Back

A horizontal line indicates that the dependent variable does not change as the independent variable changes; it represents a constant value.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you interpret a graph showing distance over time?

Back

A graph showing distance over time can be interpreted to understand speed and motion. The steeper the line, the faster the object is moving.

Front

What does a steep slope indicate in a distance-time graph?

Back

A steep slope in a distance-time graph indicates a high speed; the object is covering a large distance in a short amount of time.