The true statement about the graph of [tex]f(x) = \frac{x^2 + 2x + 1}{2x^2 - 10x+12}[/tex] is (c) its vertical asymptote are x = 3 and x = 2
The function is given as:
[tex]f(x) = \frac{x^2 + 2x + 1}{2x^2 - 10x+12}[/tex]
Set the denominator to 0
2x^2 - 10x + 12 = 0
Divide through by 2
x^2 - 5x + 6 = 0
Expand
x^2 - 2x - 3x + 6 = 0
Factorize
(x - 2)(x - 3) = 0
Solve for x
x = 2 or x = 3
The above represents the vertical asymptote of the graph
Hence, the vertical asymptote are x = 3 and x = 2
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