Given the graph of $f ,$ describe how the graph of $y = \frac { 4 } { 3 } f ( x - 3 ) + \frac { 4 } { 3 }$ can be obtained from the graph of $f$
A) Shift $\frac { 4 } { 3 }$ units to the right, then stretching vertically by a factor of
$3$ , then shift upward
$\frac { 4 } { 3 }$ units.
B) Shift $3$ units to the right, then shrinking horizontally by a factor of
$\frac { 4 } { 3 }$ , then shift downward
$\frac { 4 } { 3 }$ units.
C) Shift $3$ units to the left, then shrinking vertically by a factor of
$\frac { 4 } { 3 }$ , then shift upward
$3$ units.
D) Shift $3$ units to the right, then stretching vertically by a factor of
$\frac { 4 } { 3 }$ , then shift upward
$\frac { 4 } { 3 }$ units.
E) Shift $3$ units to the left, then shrinking vertically by a factor of
$3$ , then shift upward
$\frac { 4 } { 3 }$ units.

Question

Quizplus · Accepted Answer

The function $y = \frac { 4 } { 3 } f ( x - 3 ) + \frac { 4 } { 3 }$ can be obtained from $f$ by performing the following transformations in order:

1. Shift $3$ units to the right: This is accomplished by replacing $x$ with $x - 3$.
2. Stretch vertically by a factor of $\frac{4}{3}$: This is accomplished by multiplying the function by $\frac{4}{3}$.
3. Shift upward $\frac{4}{3}$ units: This is accomplished by adding $\frac{4}{3}$ to the function.

Therefore, the correct answer is (D).

Given the Graph Of f,f ,f, Describe How the Graph Of y=43f(x−3)+43y = \frac { 4 } { 3 } f ( x - 3 ) + \frac { 4 } { 3 }y=34​f(x−3)+34​

Given the Graph Of $f ,$ Describe How the Graph Of $y = \frac { 4 } { 3 } f ( x - 3 ) + \frac { 4 } { 3 }$