what is the domain of f(x)? what is the it's range f(x)=8/x+9

Question

1. what is the domain of f(x)? what is the it's range f(x)=8/x+9

 

2.Explain how the graph of f can be obtain from the graph of y=I/x   f(x)=2/x

Answer 1

Domain is the set of x values in which the function exists.  Range is the set of y values in which the function exists.

 

f(x) = 8 / (x + 9)

 

 

Since the denominator cannot be zero, we set the denominator equal to zero. 

 

x + 9 = 0

 

x = -9

 

 

The domain is all real numbers except for -9.

 

To find the range, we evaluate f(x) as x approaches negative infinity and infinity from both directions.   Keep in mind that -9 is not in the domain, so we cannot evaluate f(-9).

 

 

Starting from x = -9.01 to x = -1000

 

f(-9.01) = 8 / (-9.01 + 9)

            = -800

 

f(-10) = 8 / (-10 + 9)

         = -8

 

f(-100) = 8 / (-100 + 9)

           = -0.879

 

f(-1000) = 8 / (-1000 + 9)

             = -0.008

 

 

 

From x = -8.99 to x = 1000

 

f(-8.99) = 8 / (-8.99 + 9)

            = 800

 

f(10) = 8 / (10 + 9)

            = 0.421

 

f(100) = 8 / (100 + 9)

          = 0.734

 

f(1000) = 8 / (1000 + 9)

           = 0.0079

 

 

Based on the calculations, as x approaches negative infinity from x= -9.01, f(x) gets closer to zero.

 

As x approaches infinity from x=-8.99, f(x) gets closer to zero.

 

 

Range is all real numbers except for zero.

 

 

2)

 

Let f(x)=y.

 

 

y = 2 / x

 

This is an inverse relationship.  As x increases, y decreases.   The domain is all real numbers except for zero.

 

Range is all real numbers except for zero.