Describe the vertical asympotote(s) and hole(s) for the graph R(x) = (x + 3)(x - 3)/(x - 3)(x - 2)?Question 13Answera.asymptote: x = 3 and hole: x = 2b.asymptote: x = -2 and hole: x = -3c.asymptote: x = 2 and x = 3d.asymptote: x = 2 and hole: x = 3
Question
Describe the vertical asympotote(s) and hole(s) for the graph R(x) = (x + 3)(x - 3)/(x - 3)(x - 2)?Question 13Answera.asymptote: x = 3 and hole: x = 2b.asymptote: x = -2 and hole: x = -3c.asymptote: x = 2 and x = 3d.asymptote: x = 2 and hole: x = 3
Solution
The function R(x) = (x + 3)(x - 3)/(x - 3)(x - 2) simplifies to R(x) = (x + 3)/(x - 2) because the (x - 3) terms cancel out.
This means that there is a hole at x = 3.
The denominator of the simplified function is (x - 2), which means the function is undefined at x = 2. This is where the vertical asymptote is.
So, the correct answer is: asymptote: x = 2 and hole: x = 3.
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