9514 1404 393
Answer:
(A) 1 only
Step-by-step explanation:
Factor numerator and denominator and see what cancels.
[tex]f(x)=\dfrac{2x^2+14x-16}{x^2-9x+8}=\dfrac{2(x-1)(x+8)}{(x-1)(x-8)}=\dfrac{x-1}{x-1}\cdot\dfrac{2(x+8)}{x-8}\\\\f(x)=\dfrac{2x+16}{x-8}\qquad x\ne1[/tex]
The factor of x-1 in the original denominator means the expression is undefined at x=1. The reduced expression is defined there, so the discontinuity at x=1 could be removed by defining f(1) = -18/7.
There is a removable discontinuity at x=1 only. The discontinuity at x=8 is a vertical asymptote where the function changes sign. It cannot be removed by defining a value for the function there.
