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 factor that cancels out in a rational function.

Tags

CCSS.HSF-IF.C.7D

Front

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

Back

To find the coordinates of a hole, set the factor that causes the hole to zero and solve for the x-value. Then, substitute this x-value into the simplified function to find the corresponding y-value.

Tags

CCSS.HSF-IF.C.7D

Front

Given the function f(x) = (x + 3)(x - 2)/(x + 3), where is the hole located?

Back

The hole is located at (-3, 0) because the factor (x + 3) cancels out.

Tags

CCSS.HSF-IF.C.7D

Front

What does it mean if a graph has no holes?

Back

If a graph has no holes, it means that the function is defined for all values in its domain and there are no points where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of identifying holes in a graph?

Back

Identifying holes helps in understanding the behavior of the function, particularly in limits and continuity.

Tags

CCSS.HSF-IF.C.7D

Front

If a function has a hole at (a, b), what does this imply about the function's continuity at that point?

Back

The function is not continuous at the point (a, b) because it is not defined there.

Front

What is the difference between a hole and a vertical asymptote?

Back

A hole indicates a point where the function is undefined due to cancellation, while a vertical asymptote indicates a point where the function approaches infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How can you determine if a point is a hole or an asymptote?

Back

Factor the function and check if the point causes a cancellation (hole) or if it leads to division by zero without cancellation (asymptote).

Tags

CCSS.HSF-IF.C.7D

Front

What is the coordinate of the hole in the function f(x) = (x + 5)(x - 1)/(x + 5)?

Back

The hole is located at (-5, 0).

Tags

CCSS.HSF-IF.C.7D

Front

If a rational function has a hole at (c, d), how do you express this in terms of limits?

Back

You can express it as lim (x -> c) f(x) = d, indicating that as x approaches c, the function approaches d, but f(c) is undefined.

Tags

CCSS.HSF-IF.C.7D