Q: Given the function $$f(x) = x^4$, what is the end behavior as x$$ \to +\infty$$ and x$$ \to -\infty$$?

As $$x \to +\infty$$, $$f(x) \to +\infty$$; as $$x \to -\infty$$, $$f(x) \to +\infty$$

Q: What is the half-life of a radioactive substance that is reduced by 30% in 20 hours?

$$t = \frac{\ln 0.5}{\ln 0.7} \times 20 \approx 38.87$$ hours

Question 1

Which of the following is the correct formula for a line with slope 2 and x-intercept 5?

Accepted Answer

$$y = 2x - 10$$

Question 2

Given the graph of $$f(x) ($$see image 1), what is the domain of $$f(x)$$?

Accepted Answer

$$[0, 7]$$

Question 3

Which of the following functions represents a parabola opening downward with vertex at $$(2, 5)$$?

Accepted Answer

$$y = -(x-2)^2$ + 5$$

Question 4

For the function $$g(x) = \frac{x^2$ - 4}{x^2$ + x}$$, where does $$g(x)$$ have a vertical asymptote?

Accepted Answer

$$x = -1$$ and $$x = 0$$

Question 5

A cosine curve has a maximum at $$(0, 5)$$ and a minimum at $$(\pi, -5). $$Which equation matches this description?

Accepted Answer

$$y = 5 \cos(x)$$

Question 6

Given $$f(n) = 3n^2$ - 2$$ and $$g(n) = n + 1$$, what is $$f(n) + g(n)$$?

Accepted Answer

$$3n^2 + n - 1$

Question 7

A culture of 100 bacteria doubles every 2 hours. How long will it take to reach 3,200 bacteria?

Accepted Answer

$$10$$ hours

Question 8

What is the equation of the line relating Fahrenheit ($$F) $$and Celsius ($$C) $$temperatures?

Accepted Answer

$$F = 1.8C + 32$$

Question 9

For the function $$y = 5 + \cos(3x)$$, what is its amplitude?

Accepted Answer

$$1$$

Question 10

Given the function $$f(x) = x^4$, what is the end behavior as x$$ 	o +\infty$$ and x$$ 	o -\infty$$?

Accepted Answer

As $$x 	o +\infty$$, $$f(x) 	o +\infty$$; as $$x 	o -\infty$$, $$f(x) 	o +\infty$$

Question 11

The yield $$Y ($$bushels) of an apple orchard as a function of fertilizer $$a ($$lbs) is shown in image 16. What does the vertical intercept represent?

Accepted Answer

The yield when no fertilizer is used

Question 12

What is the average rate of change of the apple yield from $$a = 0 to$$ $$a = 50$$ lbs (see image 16)?

Accepted Answer

$$6$$ bushels per pound

Question 13

Which of the following best describes the end behavior of $$f(x) = \frac{5x^2$ + 3x}{x^2$ + 6} as$$ $$x 	o \infty$$?

Accepted Answer

$$f(x) 	o 5$$

Question 14

If prices are increasing at 5% per year, what is the doubling time?

Accepted Answer

$$t = \frac{\ln 2}{\ln 1.05} \approx 14.21$$ years

Question 15

Given the graph of $$y = 5 \sin\left(\frac{1}{3}x\right) ($$see image 17), what is the period of the function?

Accepted Answer

$$6\pi$$

Question 16

Which of the following is the correct formula for a cubic polynomial with $$x-$$intercepts at $$1$$, $$5$$, and $$7$$?

Accepted Answer

$$y = (x-1)(x-5)(x-7)$$

Question 17

For the function $$g(x) = \frac{x^2$ - 4}{x^2$ + x}$$, what is the horizontal asymptote?

Accepted Answer

$$y = -1$$

Question 18

What is the half-life of a radioactive substance that is reduced by 30% in 20 hours?

Accepted Answer

$$t = \frac{\ln 0.5}{\ln 0.7} 	imes 20 \approx 38.87$$ hours

Math 261 Study Guide: Functions, Graphs, and Calculus Concepts

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