A continuous function y = f(x) is known to be negative at x = 5 and positive at x = 8. Why does the equation f(x) = 0 have at least one solution between x = 5 and x = 8? Illustrate with a sketch. Why does the equation f(x) = 0 have at least one solution between x = 5 and x = 8? O A. f(x)=0 has at least one solution between x = 5 and x = 8 because f(x) must pass through all values between f(5) and f(8), regardless of whether f is continuous. O B. f(x) = 0 has at least one solution between x = 5 and x = 8 because f is a continuous function on the closed interval [5, 8], and if yo is any value between f(5) and f(8), then yo = f(c) for some c in [5, 8]. O c. f(x)=0 has at least one solution between x = 5 and x = 8 because all continuous functions have at least one zero over any nonempty closed interval. Choose a graph below that illustrates the situation. O A. 2- Q x Q ✔ OB. Q OC. -2- Q O D. 2-

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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A continuous function y = f(x) is known to be negative at x = 5 and positive at x = 8. Why does the equation f(x) = 0 have at least one solution between x = 5 and x = 8? Illustrate with a sketch.
Why does the equation f(x) = 0 have at least one solution between x = 5 and x = 8?
A. f(x) = 0 has at least one solution between x = 5 and x = 8 because f(x) must pass through all values between f(5) and f(8), regardless of whether f is continuous.
B. f(x) = 0 has at least one solution between x = 5 and x = 8 because f is a continuous function on the closed interval [5, 8], and if y is any value between f(5) and f(8), then yo = f(c) for some c in [5, 8].
C. f(x) = 0 has at least one solution between x = 5 and x = 8 because all continuous functions have at least one zero over any nonempty closed interval.
Choose a graph below that illustrates the situation.
A.
AY
2-
0
ST
▬▬
X
LO
B.
Ay
2-
0
=
L
C.
Ay
2-
10
D.
2-
-2-
ENE
=
10
Transcribed Image Text:A continuous function y = f(x) is known to be negative at x = 5 and positive at x = 8. Why does the equation f(x) = 0 have at least one solution between x = 5 and x = 8? Illustrate with a sketch. Why does the equation f(x) = 0 have at least one solution between x = 5 and x = 8? A. f(x) = 0 has at least one solution between x = 5 and x = 8 because f(x) must pass through all values between f(5) and f(8), regardless of whether f is continuous. B. f(x) = 0 has at least one solution between x = 5 and x = 8 because f is a continuous function on the closed interval [5, 8], and if y is any value between f(5) and f(8), then yo = f(c) for some c in [5, 8]. C. f(x) = 0 has at least one solution between x = 5 and x = 8 because all continuous functions have at least one zero over any nonempty closed interval. Choose a graph below that illustrates the situation. A. AY 2- 0 ST ▬▬ X LO B. Ay 2- 0 = L C. Ay 2- 10 D. 2- -2- ENE = 10
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