Question 1

Which of the following is NOT a requirement for a function $$f(x) to be $$continuous at $$x = c$$?

Accepted Answer

$$f(x) is $$differentiable at $$x = c$$

Question 2

Given $$f(x) = x^2$ - 9$$, for which values of $$x is$$ $$f(x)$$ continuous?

Accepted Answer

For all $$x$$

Question 3

A bakery estimates its annual profit by $$P(x) = 6x - 0.001x^2$ - 5000$$, where $$x is $$the number of loaves sold. For which interval of $$x$$ does the bakery make a positive profit?

Accepted Answer

$$1000 \u003c x \u003c 5000$$

Question 4

Which of the following functions is NOT continuous for all real numbers?

Accepted Answer

$$f(x) = \frac{1}{x-2}$$

Question 5

Consider $$f(x) = \frac{x+1}{x-2}. $$For which intervals is $$f(x)$$ positive?

Accepted Answer

$$(-\infty, -1)$$ and $$(2, \infty)$$

Question 6

If $$f(x) is $$continuous on $$(a, b)$$ and $$f(x) 
eq 0$$ for all $$x in$$ $$(a, b)$$, what can be said about the sign of $$f(x) on$$ $$(a, b)$$?

Accepted Answer

$$f(x) is $$either always positive or always negative on $$(a, b)$$

Question 7

Which of the following is a partition number for the function $$f(x) = \frac{x+1}{x-2}$$?

Accepted Answer

$$x = -1$$ and $$x = 2$$

Question 8

For the function $$f(x) = \sqrt{x+1}$$, on which interval is $$f(x)$$ continuous?

Accepted Answer

$$[-1, \infty)$$

Question 9

Suppose $$f(x) is $$continuous everywhere and $$f(2) = 5. If$$ $$f(x) 
eq 0$$ for all $$x in$$ $$(1, 8)$$, can $$f(x) be $$negative for any $$x in$$ $$(1, 8)$$?

Accepted Answer

No, $$f(x)$$ must be positive for all $$x in$$ $$(1, 8)$$

Question 10

Which property is true for the sum of two functions that are continuous on the same interval?

Accepted Answer

Their sum is continuous on the same interval

Question 11

Given $$f(x) = (x-3)(x+1)$$, where is $$f(x)$$ discontinuous?

Accepted Answer

Nowhere; $$f(x) is $$continuous for all $$x$$

Question 12

If $$f(x) is $$continuous on $$[a, b]$$, which of the following must be true?

Accepted Answer

$$f(x) is $$continuous on $$(a, b)$$ and continuous on the right at $$a$$ and on the left at $$b$$

Question 13

Which of the following is true about rational functions?

Accepted Answer

They are continuous everywhere except where the denominator is zero

Question 14

For $$f(x) = |x-1|/(x-1)$$, at which point is $$f(x)$$ discontinuous?

Accepted Answer

$$x = 1$$

Question 15

Which of the following is a correct step in constructing a sign chart for a function $$f(x)$$?

Accepted Answer

Find all partition numbers where $$f(x) is $$discontinuous or $$f(x) = 0$$

Question 16

If $$f(x) = x^n$$ for $$n a $$positive integer, which statement is true?

Accepted Answer

$$f(x) is $$continuous for all $$x$$

Continuity and Sign Charts in Business Calculus

Guida di studio - Domande di pratica

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