Domain and Range from Graphs Review

Front

What is the definition of domain in 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 definition of range in 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 can you determine the domain of a graph?

Back

To determine the domain of a graph, identify the x-values that the graph covers. Look for any restrictions such as vertical asymptotes or holes.

Front

How can you determine the range of a graph?

Back

To determine the range of a graph, identify the y-values that the graph covers. Look for any restrictions such as horizontal asymptotes or gaps.

Front

What is a vertical line test and how is it used?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a horizontal line test and how is it used?

Back

The horizontal line test is used to determine if a function is one-to-one. If a horizontal line intersects the graph at more than one point, the function is not one-to-one.

Front

What are the common types of functions and their general domains?

Back

Common types of functions include linear (all real numbers), quadratic (all real numbers), and rational (all real numbers except where the denominator is zero).

Front

What is the significance of asymptotes in determining domain and range?

Back

Asymptotes indicate values that the function cannot reach, affecting both the domain (for vertical asymptotes) and the range (for horizontal asymptotes).

Front

How do you find the domain of a rational function?

Back

To find the domain of a rational function, set the denominator equal to zero and solve for x. The domain includes all real numbers except those values.

Front

How do you find the range of a quadratic function?

Back

The range of a quadratic function can be determined by finding the vertex and identifying whether the parabola opens upwards or downwards.