题目
题目

MATH-112-301-001 Unproctored Midcourse 1 Practice Exam 1

单项选择题

Consider the function g(x)= 1 x  on the interval [−1,1]. We know that g(−1)=−1 and g(1)=1. Which of the following statements is correct?

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标准答案
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思路分析
To begin, let's clarify the problem setup and what the Intermediate Value Theorem (IVT) requires. The function g is described as g(x) = 1/x on the interval [-1, 1]. A key detail is that 1/x is not defined at x = 0, so g is not defined (and hence not continuous) on the entire closed interval [-1, 1]. Next, consider what IVT needs: a function must be ......Login to view full explanation

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类似问题

Let [math: f] be a continuous function defined on the domain [math: [0,2]][0,2]. If [math: f(0)=1] and [math: f(2)=3], then the equation [math: f(x)=0] has no solution.

We will discuss the Intermediate Value Theorem Links to an external site. in more detail during class. However, here is a warm-up question which will help you prepare for class: Which of the following statements are TRUE?  a) If 𝑓 ( 𝑥 ) is continuous on the interval [ 0 , 5 ] and 𝑓 ( 0 ) = 1 and 𝑓 ( 5 ) = 2 , then the Intermediate Value Theorem says that there is a number 𝑐 in [ 0 , 5 ] such that 𝑓 ( 𝑐 ) = 2 . [ Select ] False True   b) If 𝑓 ( 𝑥 ) is continuous on the interval [ 2 , 4 ]  and 𝑓 ( 2 ) < 0  and 𝑓 ( 4 ) > 0 , then the Intermediate Value Theorem says that 𝑓 ( 3 ) = 0 .  [ Select ] True False   c) If 𝑓 ( 𝑥 ) is any function and 𝑓 ( 𝑎 ) = 4  and 𝑓 ( 𝑏 ) = 6 , then the Intermediate Value Theorem says that there is a number 𝑐 in [ 𝑎 , 𝑏 ]  satisfying 𝑓 ( 𝑐 ) = 5 . [ Select ] True False

Consider the function 𝑔 ( 𝑥 ) = 1 𝑥  on the interval [ − 1 , 1 ] . We know that 𝑔 ( − 1 ) = − 1 and 𝑔 ( 1 ) = 1 . Which of the following statements is correct?

Suppose that 𝑓 ( 𝑥 ) is a function that is a rational function and its domain is ( − ∞ , − 3 ) ∪ ( − 3 , 0 ) ∪ [ 0 , ∞ )  . Also suppose that 𝑓 ( 2 ) = − 1 and 𝑓 ( 4 ) = 1 . What may we conclude about 𝑓 ( 𝑥 ) ? (There is only one correct answer.)

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