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) =

Question

Allushta

13 days ago

9

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?

Mathematics

2 answers:

AnnZ [3.8K] · Answer 1 · 2026-02-20T18:40:36+03:00

AnnZ [3.8K]13 days ago

7 0

Answer:

The graph has been shifted 4 units to the left and 6 units downward.

I completed the test!

lawyer [4K] · Answer 2 · 2026-02-20T18:43:19+03:00

The adjusted equation $g(x)=\frac{1}{x+4}-6$ , indicating that the graph has been altered 4 units leftward and 6 units downward.

Clarification:

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

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

Applying the function transformation rules, it's clear that the parent function $f(x)=\frac{1}{x}$ has been modified into the function $g(x)=\frac{1}{x+4}-6$ .

According to the function transformation rules,

$f(x+b)$ indicates shifting the function b units to the left.

Thus, the transformed function reflects a shift 4 units to the left.

Additionally, from the function transformation rules, we understand that,

$f(x)-b$ indicates shifting the function b units downward.

Consequently, the transformed function mirrors a shift of 6 units downward.

In summary, the adjusted equation $g(x)=\frac{1}{x+4}-6$ , shows the graph shifted 4 units to the left and 6 units downward.