Q: What is the domain and the range of the function $$g(x) = x + 5$$?

Domain: $$(-\infty, \infty)$$ \n Range: $$(-\infty, \infty)$$

Question 1

What is the domain and the range of the function $$g(x) = x + 5$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$ 
 Range: $$(-\infty, \infty)$$

Question 2

For the function $$f(x) = \frac{5x + 15}{x - 3}$$, what are the equations of all possible asymptotes?

Accepted Answer

$$x = 3$$ and $$y = 5$$

Question 3

Given $$f(x) = 5 + 7x$$, which of the following is the correct inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{1}{7}x - \frac{5}{7}$$

Question 4

Is the following trigonometric equation an identity? 
 $$\frac{\cos A}{1 - \sin A} = \frac{1 + \sin A}{\cos A}$$

Accepted Answer

An identity

Question 5

Which of the following pairs of $$u(x)$$ and $$v(x) is $$correct for $$v(u(x)) = (x^4$ - 5)^9$?

Accepted Answer

$$u(x) = x^4$ - 5$$ and $$v(x) = x^9$

Question 6

Simplify the expression $$(10/5)^{-3}.$$

Accepted Answer

1/8

Question 7

A certain species of fish in a lake reproduces at a rate that doubles its population every 24 hours. If the initial population is 200, what will be the population 3 days after the initial observation? Use $$p(t) = 200 \cdot 2$$^{t}$$, where t$ is in days.

Accepted Answer

1600

Question 8

Given $$\log_{a} a = 0.45$$ and $$\log_{b} b = 0.65$$, find the value of $$\log_{a}(a/b).$$

Accepted Answer

0.20

Question 9

Identify the intervals where the function $$h(x) = x^4$ - 4 is $$one-to-one and thus has an inverse.

Accepted Answer

$$(-\infty, -4)$$ and $$(4, \infty)$$

Question 10

Which of the following is equivalent to $$\csc$$^{-1}$$(y)$$ for $$y 
eq 0$$?

Accepted Answer

$$\sin$$^{-1}$$(1/y)$$

Question 11

Evaluate the limit: $$\lim_{x 	o 0} 11e^x \cos x.$$

Accepted Answer

11

Question 12

Prove the limit statement: $$\lim_{x 	o 2} (7 - x) = 5. $$Which of the following choices for $$\delta (in $$terms of $$\epsilon) $$correctly proves this limit?

Accepted Answer

$$\delta = \epsilon$$

Question 13

A real-world application: The temperature $$T (in$$ °C) of a chemical reaction is modeled by $$T(t) = 20 + 15e$$^{-0.2t}$$, where t$ is time in minutes. What is the temperature after 10 minutes?

Accepted Answer

$$T(10) = 20 + 15e$$^{-2}$$ \approx 22.0$$

Question 14

Which of the following graphs represents a function that is continuous on the interval $$(0, 15)$$?

Accepted Answer

A graph with no breaks, jumps, or holes in $$(0, 15)$$

Calculus Midterm Study Guide: Functions, Limits, and Continuity

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