Answer:
Given the function: [tex]y= -2(3)^x[/tex] .....[1]
An exponential function is in the form of [tex]y=ab^x[/tex].
- If [tex]a< 0[/tex] and b <1, then the graph is increasing
- If a< 0 and b >1 , then the graph is decreasing.
- If a> 0 and b<1, the the graph is decreasing.
- if a< 0 and b > 1. then the graph is increasing.
From the given equation [1] we have;
Here, a = -2 < 0 and b = 3 > 1.
For this function, x-intercepts doesn't exist, as it does not crosses the x-axis graph.
y-intercept states that the graph crosses the y-axis.
Substitute value of x =0 in [1] to solve for y;
[tex]y = -2(3)^0[/tex]
y = -2
y-intercept = (0, -2)
End Behavior of the given graph :
If [tex]x \rightarrow \infty[/tex] , then [tex]f(x) \rightarrow -\infty[/tex]
and
If [tex]x \rightarrow -\infty[/tex], then [tex]f(x) \rightarrow 0[/tex]
Also, You can see the graph as shown below in the attachment.
