Answer:
Option D is correct.
Step-by-step explanation:
An exponential function is in the form of [tex]y =ab^x[/tex] where a is the initial value and b≠ 0 , b >1 .
Given: The function f(x) = y = [tex]4 \cdot 3^x[/tex] ......[1]
The domain is all real numbers and the range is y > 0.
y-intercept defined as the graph crosses the y-axis.
Substitute the value of x= 0 in [1] to solve for y;
y = [tex]4 \cdot 3^0[/tex] = 4
y-intercept = (0, 4)
End behavior:
when b =3 >1
then;
as [tex]x \rightarrow \infty[/tex] , [tex]f(x)\rightarrow \infty[/tex]
as [tex]x \rightarrow -\infty[/tex] , [tex]f(x)\rightarrow 0[/tex]
therefore, the only graph which represents the function y = [tex]4 \cdot 3^x[/tex] is Option D
