Explain how the graph of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$ is obtained from the graph of $f = | x |$ .
A) Shift the graph of $f$ one unit to the right, then shift downward
$\frac { 2 } { 3 }$ units.
B) Shift the graph of $f$ one unit to the right, then shift downward
$2$ units.
C) Shift the graph of $f$ one unit to the left, then shrink vertically by a factor of
$\frac { 2 } { 3 }$ .
D) Shift the graph of $f$ one unit to the left, then shift upward
$\frac { 2 } { 3 }$ units.
E) Shift the graph of $f$ one unit to the left, shrink vertically by a factor of
$\frac { 1 } { 3 }$ , shift downward
$\frac { 2 } { 3 }$ units.

Question

Quizplus · Accepted Answer

The graph of $g(x) = \frac{|x + 1| - 2}{3}$ is obtained from $f = |x|$ by first shifting $f$ one unit to the left (to account for $|x + 1|$), then shrinking it vertically by a factor of $\frac{1}{3}$ (because of the division by 3), and finally shifting it downward by $\frac{2}{3}$ units (to account for the $-2$ in the numerator divided by 3).

Explain How the Graph Of g(x)=∣x+1∣−23g ( x ) = \frac { | x + 1 | - 2 } { 3 }g(x)=3∣x+1∣−2​

Explain How the Graph Of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$