题目
题目

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

单项选择题

Consider the function  on the interval . We know that and . Which of the following statements is correct?

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标准答案
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思路分析
We are asked to consider a function on a given interval and are told two bits of information: the function values at endpoints (although these values are not explicitly shown in the prompt here) and we must determine which statement is correct. First, notice that the provided answer set is incomplete: there are no answer options listed beyond the single item in the answer field, which states that the Intermediate Val......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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