The range of the function f(x) is (-ā, 3]
The function definition is given as:
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
There are two sub-functions and the domains in the above definition.
Each function would be plotted alongside its domain.
See attachment for the graph of the function f(x)
From the graph of the function, we have the following range of f(x)
Minimum = Negative Infinity
Maximum = 5
Hence, the range of the function f(x) is (-ā, 3]
We have the domains to be
x <= 3 and x > 3
This means that the asymptote of f(x) is x = 3
From the graph, we have:
This means that the end behavior of f(x) is as x approaches +ā, the function approaches +ā and as x approaches -ā, the function approaches -ā
Read more about functions at:
https://brainly.com/question/27262465
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Complete question
A piecewise function f (x) is defined by
[tex]f(x) = \left[\begin{array}{cc}3^{x-1}-4&x\le 3\\ \frac{-x^2 + 3x + 4}{x^2 - 7x + 12}&x > 3\end{array}\right[/tex]
