Question

The graph of g(x) is transformed from its parent function, f(x). Apply concepts involved in determining the key features of a rational function to determine the domain and range of the function, .

A. What is the domain of the function, g(x)?
B. What is the range of the function, g(x)?

Answer 1

We are given the function:

$g(x) = \frac{1}{x-6}$

Domain:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

In case of fractions, we must not have the denominator as zero , otherwise the function will become undefined.

So equating denominating equal to zero to find restriction.

$x-6=0$

x=6

So at x=6 , the function becomes undefined.

So domain is all real numbers except x=6.

Range:

For a fraction, we find domain of inverse function and that gives the range.

$g(x) = \frac{1}{x-6}$

replacing g(x) by y

$y = \frac{1}{x-6}$

switching y by x and x by y

$x = \frac{1}{y-6}$

solving for y,

$y=\frac{1}{x} +6$

Now here we find domain of this function.

Again for a fraction denominator cannot be zero

So range is :

g(x) >0 and g(x) <0

Answer 2

Answer:

A.f(x) = (one-half) Superscript x  D.The domains of both functions are the same    E.The translation from f(x) to g(x) is right 4 units and down 2 units.  

Step-by-step explanation:

A. D. E.