Question

Write the equation of G(x)

Answer 1

Answer:

The equation is

$G(x)=-\frac{1}{2}(x-3)^3 +2$

Step-by-step explanation:

If the graph of the function $G(x)=cf(x+h) +b$  represents the transformations made to the graph of $y= f(x)$  then, by definition:

If  $0$ then the graph is compressed vertically by a factor c.

If  $|c| > 1$ then the graph is stretched vertically by a factor c

If $c$  then the graph is reflected on the x axis.

If $b> 0$ the graph moves vertically upwards.

If $b$ the graph moves vertically down

If $h$ the graph moves horizontally h units to the right

If $h >0$ the graph moves horizontally h units to the left

In this problem we have the function $G(x)$ and our parent function is $f(x) = x^3$

We know that G(x) is equal to f(x) but reflected on the x-axis ($c$), compressed vertically by a multiple of 1/2 ($0$ and $c = -\frac{1}{2}$), displaced 2 units upwards ($b = 2>0$) and moved to the right 3 units ($h = -3$)

Then:

$G(x)=-\frac{1}{2}f(x-3) +2$

$G(x)=-\frac{1}{2}(x-3)^3 +2$

Answer 2

Answer:

$G(x)=\frac{1}{2}(x-3)^3+2$

Step-by-step explanation:

The given function is

$F(x)=x^{3}$

The transformations to this graph are  in the form;

$G(x)=a(x-b)^3+c$

where $a=\frac{1}{2}$ is the vertical compression by a factor of $\frac{1}{2}$

b=3 is a shift to the right by 3 units.

c=2 is an upward shift by 2 units.

Therefore $G(x)=\frac{1}{2}(x-3)^3+2$