The value of k affects the position of the horizontal asymptote in the exponential function [tex]f(x) = ab^{(x-h)}+k[/tex]
The horizontal asymptote is a horizontal line that does not touch the x-axis but is sufficiently close to it in order to determine the value of x
Note:
For an exponential function of the form [tex]f(x)=ab^x+c[/tex]:
The horizontal asymptote is y = c
The given exponential function is:
[tex]f(x) = ab^{(x-h)}+k[/tex]
Applying the rule stated above to the given function [tex]f(x) = ab^{(x-h)}+k[/tex], the horizontal asymptote of the function f(x) is y = k
Therefore, the value of k affects the position of the horizontal asymptote in the exponential function [tex]f(x) = ab^{(x-h)}+k[/tex]
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