A continuous function y = f(x) is known to be negative at x= 4 and positive at x = 9. Why does the equationf(x) = 0 have at least one solution between x= 4 and x= 9? Illustrate with a sketch.Why does the equation f(x) = 0 have at least one solution between x= 4 and x= 9?O A. f(x) = 0 has at least one solution between x= 4 and x= 9 because f is a continuous function on theclosed interval [4, 9], and if y, is any value between f(4) and f(9), then yo = f(c) for some c in [4, 9].O B. f(x) = 0 has at least one solution between x= 4 and x= 9 because f(x) must pass through all valuesbetween f(4) and f(9), regardless of whether f is continuous.OC. f(x) = 0 has at least one solution between x= 4 and x= 9 because all continuous functions have atleast one zero over any nonempty closed interval.Choose a graph below that illustrates the situation.O A.OC.B.D.Ay2-Ay2-2-2-101010

Question
Asked Dec 15, 2019
77 views

*show work*

A continuous function y = f(x) is known to be negative at x= 4 and positive at x = 9. Why does the equation
f(x) = 0 have at least one solution between x= 4 and x= 9? Illustrate with a sketch.
Why does the equation f(x) = 0 have at least one solution between x= 4 and x= 9?
O A. f(x) = 0 has at least one solution between x= 4 and x= 9 because f is a continuous function on the
closed interval [4, 9], and if y, is any value between f(4) and f(9), then yo = f(c) for some c in [4, 9].
O B. f(x) = 0 has at least one solution between x= 4 and x= 9 because f(x) must pass through all values
between f(4) and f(9), regardless of whether f is continuous.
OC. f(x) = 0 has at least one solution between x= 4 and x= 9 because all continuous functions have at
least one zero over any nonempty closed interval.
Choose a graph below that illustrates the situation.
O A.
OC.
B.
D.
Ay
2-
Ay
2-
2-
2-
10
10
10
help_outline

Image Transcriptionclose

A continuous function y = f(x) is known to be negative at x= 4 and positive at x = 9. Why does the equation f(x) = 0 have at least one solution between x= 4 and x= 9? Illustrate with a sketch. Why does the equation f(x) = 0 have at least one solution between x= 4 and x= 9? O A. f(x) = 0 has at least one solution between x= 4 and x= 9 because f is a continuous function on the closed interval [4, 9], and if y, is any value between f(4) and f(9), then yo = f(c) for some c in [4, 9]. O B. f(x) = 0 has at least one solution between x= 4 and x= 9 because f(x) must pass through all values between f(4) and f(9), regardless of whether f is continuous. OC. f(x) = 0 has at least one solution between x= 4 and x= 9 because all continuous functions have at least one zero over any nonempty closed interval. Choose a graph below that illustrates the situation. O A. OC. B. D. Ay 2- Ay 2- 2- 2- 10 10 10

fullscreen
check_circle

Expert Answer

Step 1

Given:

A continuous function y = f (x) is known to be negative at x = 4 and positive at x = 9.

 

Step 2

Concept used:

Intermediate Value Theorem said that:

If f (x) is a continuous function on [a, b], then for every k between f (a) and f (b), there exists a value c belongs to (a, b) such that f (c) = k.

Step 3

By Intermediate Value Theorem, f (x) = 0 has at least one solution between...

help_outline

Image Transcriptionclose

If y, is any value between f (7) and f(9), then y, = f (c) %3D for some c in (7,9). Therefore, the correct option is A. The graph D is illustrates this situation.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in