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

Answer:

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

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Answer 2

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

Explanation:

The parent equation is $f(x)=\frac{1}{x}$

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

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

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  $g(x)=\frac{1}{x+4}-6$ , the graph is shifted 4 units to the left and 6 units down.