Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

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) = StartFracti

Home/Math/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) = StartFracti

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) = StartFracti

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?

The transformed equation [tex]$g(x)=\frac{1}{x+4}-6$[/tex] , the graph is shifted 4 units to the left and 6 units down.

Explanation:

The parent equation is [tex]$f(x)=\frac{1}{x}$[/tex]

The transformed equation is [tex]$g(x)=\frac{1}{x+4}-6$[/tex]

By using the function transformation rules, we can see that the parent function [tex]$f(x)=\frac{1}{x}$[/tex] is transformed into the function [tex]$g(x)=\frac{1}{x+4}-6$[/tex]

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

[tex]$f(x+b)$[/tex] 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,

[tex]$f(x)-b$[/tex] shifts the function b units downward.

Thus, the transformed function is shifted 6 units down.

Thus, the transformed equation [tex]$g(x)=\frac{1}{x+4}-6$[/tex] , the graph is shifted 4 units to the left and 6 units down.

## Answers ( )

The transformed equation [tex]$g(x)=\frac{1}{x+4}-6$[/tex] , the graph is shifted 4 units to the left and 6 units down.

Explanation:The

parent equationis [tex]$f(x)=\frac{1}{x}$[/tex]The

transformed equationis [tex]$g(x)=\frac{1}{x+4}-6$[/tex]By using the

function transformation rules, we can see that the parent function [tex]$f(x)=\frac{1}{x}$[/tex] is transformed into the function [tex]$g(x)=\frac{1}{x+4}-6$[/tex]Since, from the function transformation rules, we know that,

[tex]$f(x+b)$[/tex] 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,

[tex]$f(x)-b$[/tex] shifts the

function b units downward.Thus, the transformed function is

shifted 6 units down.Thus,

the transformed equation[tex]$g(x)=\frac{1}{x+4}-6$[/tex], the graph is shifted 4 units to the left and 6 units down.Answer:the graph is shifted 4 units to the left and 6 units down.

I took the test!