Pre-Algebra Examples

$f (n) = \frac{2^{n}}{10^{6}}$

Step 1

Find where the expression $\frac{2^{x}}{1000000}$ is undefined.

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Step 2

The vertical asymptotes occur at areas of infinite discontinuity.

No Vertical Asymptotes

Step 3

Evaluate $lim_{x \to - \infty} \frac{2^{x}}{1000000}$ to find the horizontal asymptote.

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Step 3.1

Move the term $\frac{1}{1000000}$ outside of the limit because it is constant with respect to $x$ .

$\frac{1}{1000000} lim_{x \to - \infty} 2^{x}$

Step 3.2

Since the exponent $x$ approaches $- \infty$ , the quantity $2^{x}$ approaches $0$ .

$\frac{1}{1000000} \cdot 0$

Step 3.3

Multiply $\frac{1}{1000000}$ by $0$ .

$0$

Step 4

List the horizontal asymptotes:

$y = 0$

Step 5

There is no oblique asymptote because the degree of the numerator is less than or equal to the degree of the denominator.

No Oblique Asymptotes

Step 6

This is the set of all asymptotes.

No Vertical Asymptotes

Horizontal Asymptotes: $y = 0$

No Oblique Asymptotes

Step 7