Only bottom left graph satisfy the conditions of the end behaviour and y-intercept. The bottom left option is correct.
Given:
The given function is:
[tex]f(x)=-\left(\dfrac{1}{3}\right)^{-x}[/tex]
To find:
The graph of the given function.
Explanation:
The given function can be rewritten as:
[tex]f(x)=-\dfrac{1}{3^{-x}}[/tex]
[tex]f(x)=-3^{x}[/tex]
For [tex]x=0[/tex], we get
[tex]f(0)=-3^{0}[/tex]
[tex]f(0)=-1[/tex]
So, the y-intercept of the graph is [tex]-1[/tex].
End behaviour of the graph:
[tex]f(x)\to 0[/tex] as [tex]x\to -\infty[/tex]
[tex]f(x)\to -\infty[/tex] as [tex]x\to \infty[/tex]
Only bottom left graph satisfy the above conditions.
Therefore, the bottom left option is correct.
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