Question

Discuss whether R is continuous at c.Use limits to analyze the graph of R at c. Graph R.

Answer 1

Step 1:

The function is , and .

The domain of a function is all values of , those makes the function mathematically correct.

The denominator of the function should not be zero.

The domain of function is all real numbers except and .

The domain of function is .

Step 2:

Rewrite the function as .

Cancel common terms.

.

The removable discontinuity is at .

is in the domain and is not in the domain.

The function is continuous every number on its domain.

Find the limit at is .

.

The hole is at .

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Step 3:

Graph the function:

Observe the graph:

As  tends to 1 from the left hand side the limit approaches to .

As  tends to 1 from the right hand side the limit approaches to .

The vertical asymptote at .

The hole at .

Solution:

.

.

.

The hole at .

The vertical asymptote at .