## 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?

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3 months 2022-02-10T08:21:31+00:00 2 Answers 0 views 0

1. 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.