F(x) = -2x^2 + 14 / x^2 - 49 which statement describes the behavior of the graph of the function shown at the vertical asymptotes? as x → –7–, y → [infinity]. as x → –7+, y → –[infinity]. as x → 7–, y → –[infinity]. as x → 7+, y → –[infinity].
Answers
Given : f(x) = (-2x² + 14)/(x² - 49)
To find : which statement describes the behavior of the graph of the function shown at the vertical asymptotes
Solution:
f(x) = (-2x² + 14)/(x² - 49)
x² - 49 = (x + 7)(x - 7)
Hence f(x) goes to infinity at x = - 7 or 7
x < - 7 = (-ve)(-ve) = + ve => x → –7– x² - 49 is + ve
-7 < x < 7 = (+ve)(-ve) = - ve => x → –7+ or x → 7– . x² - 49 is - ve
x > 7 = (+ve)(+ve) = + ve => x → 7+ x² - 49 is + ve
(-2x² + 14) is - ve for all x → –7– , x → –7+ , x → 7– , x → 7+
as -2(-7)² + 14 = -84 and -2(+7)² + 14 = -84
x → –7– = (-ve)/(+ve) => y → -[infinity].
x → –7+ or x → 7– = (-ve)/(-ve )=> y → [infinity]
x → 7+ = (-ve)/(+ve) => y → -[infinity].
x → 7+, y → –[infinity]. is the correct option
See the attached graph
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Answer:idk
Step-by-step explanation: I need help too lol