Question

question 12 of 12 step 1 of 2 no time limit
consider the following function.
$r(x)=(x - 2)^3$
step 1 of 2: graph the original function by indicating how the more basic function has been shifted, reflected, stretched, or compressed.
answer 5 points keypad keyboard shortcuts
select the type of transformations to create the correct graph. any further inputs required to complete the transformations will appear when the appropriate selection is made.
horizontal shift
left right none
vertical stretch/compress
stretch compress none
x - axis reflection
yes no
y - axis reflection
yes no
vertical shift
up down none

Explanation:

Step1: Recall the transformation rules

For a function \(y = f(x - h)\), it is a horizontal shift of the function \(y = f(x)\). If \(h>0\), the shift is to the right by \(h\) units. For the function \(r(x)=(x - 2)^{3}\), compared to the basic function \(y=x^{3}\), we have \(h = 2\).

Step2: Check other transformation types

For vertical stretch/compress, if \(y=af(x)\), \(|a|> 1\) is a stretch and \(0<|a|<1\) is a compress. Here \(a = 1\), so there is no vertical stretch/compress. For \(x\) - axis reflection \(y=-f(x)\) and \(y\) - axis reflection \(y = f(-x)\), our function \(r(x)=(x - 2)^{3}\) does not have these forms. For vertical shift \(y=f(x)+k\), here \(k = 0\).

Answer:

Horizontal Shift: Right
Vertical Stretch/Compress: None
x - Axis Reflection: No
y - Axis Reflection: No
Vertical Shift: None