Question

graph the function ( y = 2^{x - 4}-5 ) using the given table of values and following the instructions below.
equation of asymptote:
( y=)
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Explanation:

Step1: Recall the general form of an exponential function

The general form of an exponential function is \(y = a\cdot b^{x - h}+k\). For the function \(y = 2^{x - 4}-5\), where \(a = 1\), \(b = 2\), \(h = 4\), and \(k=-5\).

Step2: Determine the horizontal asymptote

For an exponential function of the form \(y=a\cdot b^{x - h}+k\), the horizontal asymptote is given by the equation \(y = k\).

Answer:

\(y=-5\)