Question

question 3 of 10
what was the equation of the graph below before it was shifted to the right
1.5 units?

graph with g(x) = (x - 1.5)³ - (x - 1.5)

a. ( g(x) = x^3 - x )
b. ( g(x) = x^3 )
c. ( g(x) = x^3 + 1.5 )
d. ( g(x) = (x - 1.5)^3 )

Explanation:

Step1: Recall horizontal shift rule

Shifting a function $f(x)$ right by $h$ units gives $f(x-h)$. To reverse a right shift of 1.5 units, replace $x$ with $x+1.5$ in the shifted function.

Step2: Apply reverse shift to given graph

The shifted function shown is $G(x)=(x-1.5)^3 - (x-1.5)$. Replace $x$ with $x+1.5$:
$G(x)=( (x+1.5)-1.5 )^3 - ( (x+1.5)-1.5 ) = x^3 - x$.

Answer:

A. $G(x) = x^3 - x$