1.10 Practice

Front

What is a hole in a graph?

Back

A hole in a graph occurs at a point where a function is not defined, typically due to a removable discontinuity. It represents a value that is not included in the domain of the function.

Front

How do you find the coordinates of a hole in a rational function?

Back

To find the coordinates of a hole, factor the numerator and denominator of the function, cancel out common factors, and set the canceled factor equal to zero to find the x-coordinate. Substitute this x-value back into the simplified function to find the y-coordinate.

Front

What does the coordinate (-5, -9) represent in a graph?

Back

The coordinate (-5, -9) represents a point on the Cartesian plane where the x-value is -5 and the y-value is -9.

Front

What is the significance of the coordinate (-3, 1/2) in relation to holes?

Back

The coordinate (-3, 1/2) indicates a hole in the graph of a function, meaning the function is not defined at x = -3, but approaches the value of 1/2 as x approaches -3.

Front

What is the difference between a hole and an asymptote in a graph?

Back

A hole is a point where a function is not defined due to a removable discontinuity, while an asymptote is a line that the graph approaches but never touches, indicating a non-removable discontinuity.

Front

What does the term 'removable discontinuity' mean?

Back

A removable discontinuity occurs when a function is not defined at a certain point, but can be made continuous by redefining the function at that point.

Front

How can you identify a hole in a rational function's equation?

Back

A hole can be identified by finding common factors in the numerator and denominator of the rational function. If a factor cancels out, it indicates a hole at the x-value that makes the canceled factor zero.

Front

What is the role of the denominator in determining holes in a function?

Back

The denominator of a function determines where the function is undefined. If the denominator equals zero at a certain x-value, it indicates a potential hole or vertical asymptote.

Front

What does the coordinate (0, 0) signify in a graph?

Back

The coordinate (0, 0) signifies the origin point in a Cartesian plane, where both x and y values are zero.

Front

What is the importance of identifying holes in a graph?

Back

Identifying holes in a graph is important for understanding the behavior of the function, particularly in calculus and limits, as it affects continuity and the function's overall shape.