Respuesta :
We are given
[tex]f(x)=x^2+4x[/tex]
h(x):
The graph of h is a translation 3 units up
so, we get
[tex]=x^2+4x+3[/tex]
2 units right of the graph of f(x)
so, we get
[tex]h(x)=(x-2)^2+4(x-2)+3[/tex]
now, we can simplify it
[tex]h(x)=x^2-4x+4+4\left(x-2\right)+3[/tex]
[tex]h(x)=x^2-1[/tex]
g(x):
we have
For each value of x, g(x) is 130% of h(x)
so, we get
g(x)=130% of h(x)
[tex]g(x)=\frac{130}{100} h(x)[/tex]
we can plug value
[tex]g(x)=\frac{130}{100} (x^2-1)[/tex]
[tex]g(x)=1.3(x^2-1)[/tex].............Answer
Answer:
The rule for g is:
[tex]g(x)=1.3(x^2-1)[/tex]
Step-by-step explanation:
The equation of the function f(x) is given by:
[tex]f(x)=x^2+4x[/tex]
Now, it is given that:
The graph of h is a translation 3 units up and 2 units right of the graph of f(x).
This means that:
[tex]h(x)=f(x-2)+3[/tex]
Hence, we have the equation for the function h(x) as:
[tex]h(x)=(x-2)^2+4(x-2)+3\\\\h(x)=x^2+4-4x+4x-8+3\\\\h(x)=x^2+4-8+3\\\\h(x)=x^2-1[/tex]
Also, g(x) is 130% of h(x).
i.e.
[tex]g(x)=130\% \ of \ h(x)\\\\g(x)=1.3h(x)\\\\g(x)=1.3(x^2-1)[/tex]
