Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
-$$f ( x ) = \frac { 1 - 7 x } { x + 3 }$$
A) Shift the graph of the reciprocal function right 3 units, stretch vertically by a factor of 22, and then shift 7 units down.
B) Shift the graph of the reciprocal function right 3 units, stretch vertically by a factor of 22, and then shift 7 units up.
C) Shift the graph of the reciprocal function left 3 units, stretch vertically by a factor of 22 , and then shift 7 units down.
D) Shift the graph of the reciprocal function left 3 units, stretch vertically by a factor of 22 , and then shift 7 units up.

Question

Quizplus · Accepted Answer

The given function can be obtained from the reciprocal function $f(x) = \frac{1}{x}$ by first shifting left 3 units (to account for the $x + 3$ in the denominator, which moves the graph left, not right), but there is no vertical stretch by a factor of 22 or shift by 7 units directly related to the form of the given function compared to the base reciprocal function. The explanation mistakenly combines transformations that don't directly apply to the given function from the base $f(x) = \frac{1}{x}$, indicating a misunderstanding of how to apply transformations to the reciprocal function. The correct transformations should focus on how the numerator and denominator affect the graph's translation, but the mention of stretching by a factor of 22 and shifting 7 units does not directly apply, indicating an error in the explanation.

Describe How the Graph of the Given Function Can Be f(x)=1−7xx+3f ( x ) = \frac { 1 - 7 x } { x + 3 }f(x)=x+31−7x​

Describe How the Graph of the Given Function Can Be $f ( x ) = \frac { 1 - 7 x } { x + 3 }$