Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
-$$f ( x ) = \frac { 2 } { x + 6 }$$
A) Shift the graph of the reciprocal function right 6 units, and then stretch vertically by a factor of 2 .
B) Shift the graph of the reciprocal function left 6 units, and then shrink vertically by a factor of $\frac { 1 } { 2 }$.
C) Shift the graph of the reciprocal function left 6 units, and then stretch horizontally by a factor of 2 .
D) Shift the graph of the reciprocal function left 6 units, and then stretch vertically by a factor of 2 .

Question

Quizplus · Accepted Answer

The graph of $f(x) = \frac{2}{x + 6}$ can be obtained from the graph of $f(x) = \frac{1}{x}$ by first shifting it left by 6 units (to account for the $x + 6$ in the denominator, which moves the graph left, not right), and then stretching it vertically by a factor of 2 (because of the 2 in the numerator, which affects the vertical scale but not the horizontal scale).

Describe How the Graph of the Given Function Can Be f(x)=2x+6f ( x ) = \frac { 2 } { x + 6 }f(x)=x+62​

Describe How the Graph of the Given Function Can Be $f ( x ) = \frac { 2 } { x + 6 }$