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.

Front

What does the graph of a function represent?

Back

The graph of a function represents the relationship between the input (x-axis) and the output (y-axis) values.

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

How do you determine the rate of change from a graph?

Back

The rate of change is determined by the slope of the line on the graph, calculated as the change in y divided by the change in x.

Front

What does a horizontal line on a graph indicate about a function?

Back

A horizontal line indicates that the function has a constant output value regardless of the input.

Front

What does a vertical line on a graph indicate?

Back

A vertical line indicates that there is no function, as it would assign multiple outputs to a single input.

Front

How can you find the intercepts of a function from its graph?

Back

The x-intercept is where the graph crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, represented by the equation y = mx + b.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line, such as quadratic or exponential functions.