Question

Consider the function g(x) = 10/x

Answer 1

Answer:

0,0

2. The domain of g(x) is the same as the domain of the parent function.

4. The range is the same as the range of the parent function.

5. The function g(x) increases over the same x-values as the parent function.

6. The function g(x) decreases over the same x-values as the parent function.

Step-by-step explanation:

Answer 2

The correct answers are:
(1) The vertical asymptote is x = 0
(2) The horizontal asymptote is y = 0

Explanation:
(1) To find the vertical asymptote, put the denominator of the rational function equals to zero.

Rational Function = g(x) = $\frac{10}{x}$

Denominator = x = 0

Hence the vertical asymptote is x = 0.

(2) To find the horizontal asymptote, check the power of x in numerator against the power of x in denominator as follows:

Given function = g(x) = $\frac{10}{x}$

We can write it as:

g(x) = $\frac{10 * x^0}{x^1}$

If power of x in numerator is less than the power of x in denomenator, then the horizontal asymptote will be y=0.
If power of x in numerator is equal to the power of x in denomenator, then the horizontal asymptote will be y=(co-efficient in numerator)/(co-efficient in denomenator).
If power of x in numerator is greater than the power of x in denomenator, then there will be no horizontal asymptote.

In above case, 0 < 1, therefore, the horizontal asymptote is y = 0