Explain how the graph of $g ( x ) = - \sqrt [ 3 ] { x + 1 }$ is obtained from the graph of $f = \sqrt [ 3 ] { x }$
A) Shift the graph of $f$ one unit to the left, then reflect about the
$y$ - axis.
B) Shift the graph of $f$ one unit to the left, then reflect about the
$y$ - axis .
C) Shift the graph of $f$ one unit up, reflect about the
$x$ - axis and stretch vertically by a factor of
$\frac { 1 } { 3 }$.
D) Shift the graph of $f$ one unit to the left, then reflect about the
$x$ - axis.
E) Shift the graph of $f$ one unit down, reflect about the
$x$ - axis and stretch vertically by a factor of
$\frac { 1 } { 3 } \text {. }$

Question

Explain how the graph of $g ( x ) = - \sqrt [ 3 ] { x + 1 }$ is obtained from the graph of $f = \sqrt [ 3 ] { x }$ 
A) Shift the graph of $f$ one unit to the left, then reflect about the
$y$ - axis.
B) Shift the graph of $f$ one unit to the left, then reflect about the
$y$ - axis .
C) Shift the graph of $f$ one unit up, reflect about the
$x$ - axis and stretch vertically by a factor of
$\frac { 1 } { 3 }$.
D) Shift the graph of $f$ one unit to the left, then reflect about the
$x$ - axis.
E) Shift the graph of $f$ one unit down, reflect about the
$x$ - axis and stretch vertically by a factor of
$\frac { 1 } { 3 } \text {. }$

Quizplus · Accepted Answer

To obtain the graph of $g(x)=-\sqrt[3]{x+1}$ from the graph of $f(x)=\sqrt[3]{x}$, we need to shift the graph of $f(x)$ one unit to the left, then reflect it about the $x$-axis. This is because the formula for the graph of $g(x)$ involves taking the cube root of $x+1$, which means that we need to shift the graph of $f(x)$ to the left by 1 unit. Moreover, the negative sign in front of the cube root in $g(x)$ indicates a reflection about the $x$-axis. Therefore, the correct choice is D.

Explain How the Graph Of g(x)=−x+13g ( x ) = - \sqrt [ 3 ] { x + 1 }g(x)=−3x+1​

Explain How the Graph Of $g ( x ) = - \sqrt [ 3 ] { x + 1 }$