Using the form g(x)=a(x−h1)+k, we want to write a that matches the given graph.
We can see that the vertical is the line
x=3. Therefore, we have that
h=3. Similarly, we see that the horizontal asymptote is the line
y=4. With this, we know that
k=4. We can write a partial equation of the function.
g(x)=a(x−31)+4
To find the value of
a, we can use any of the points on the curve. For simplicity, we will use the point
(2,1). Therefore, we will substitute
2 for
x and
1 for
g(x), and solve for
a.
g(x)=a(x−31)+4
1=a(2−31)+4
1=a(-11)+4
1=a(-1)+4
1=-a+4
-3=-a
3=a
a=3
Finally, we can write the desired equation.
g(x)=3(x−31)+4