Question

How does the graph of g (x) = StartFraction 1 Over x + 4 EndFraction minus 6 compare to the graph of the parent function f (x) = StartFraction 1 Over x EndFraction?

Answer 1

the graph is shifted 4 units to the left and 6 units down.

I took the test!

Answer 2

The transformed equation
`$g(x)=(1)/(x+4)-6$` , the graph is shifted 4 units to the left and 6 units down.

Step-by-step explanation:

The parent equation is
`$f(x)=(1)/(x)$`

The transformed equation is
`$g(x)=(1)/(x+4)-6$`

By using the function transformation rules, we can see that the parent function
`$f(x)=(1)/(x)$` is transformed into the function
`$g(x)=(1)/(x+4)-6$`

Since, from the function transformation rules, we know that,

`$f(x+b)$` shifts the function b units to the left.

Thus, the transformed function is shifted 4 units to the left.

Also, from the function transformation rules, we know that,

`$f(x)-b$` shifts the function b units downward.

Thus, the transformed function is shifted 6 units down.

Thus, the transformed equation
`$g(x)=(1)/(x+4)-6$` , the graph is shifted 4 units to the left and 6 units down.