26. Determine the point where the asymptotes of the graphs $y=b^{x-1}+2$ and $y=\log _{b}(x-1)+2$ intersect.
a) $(1,1)$
b) $(1,2)$
c) $\left(\frac{1}{2}, 2\right)$
d) $(2,1)$
e) $(2,2)$

Answer

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Answer

$\boxed{(1, 2)}$

Steps

Step 1 ：First, we find the asymptotes of the given functions.

Step 2 ：For the function $y = b^{x-1} + 2$, the horizontal asymptote is $y = 2$.

Step 3 ：For the function $y = \log_b(x-1) + 2$, the vertical asymptote is $x = 1$.

Step 4 ：Thus, the intersection point of the asymptotes is $(1, 2)$.

Step 5 ：$\boxed{(1, 2)}$