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

Question 1

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

Accepted Answer

$$[0, 7]$$

Question 2

For the function in the first image, on which interval is $$f(x)$$ decreasing?

Accepted Answer

$$(1, 7)$$

Question 3

What is the equation of the line shown in the second image?

Accepted Answer

$$y = -\frac{3}{7}x + 3$$

Question 4

Which of the following best describes the function in the third image?

Accepted Answer

$$y = e$$^{x/2}$$

Question 5

Given the fourth image, what is the value of $$y$$ when $$t = 0$$?

Accepted Answer

$$y = 3$$

Question 6

Which equation best fits the parabola in the fifth image?

Accepted Answer

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

Question 7

The function in the sixth image passes through $$(0,2)$$ and $$(2,1). $$Which of the following is a possible formula?

Accepted Answer

$$y = 2e$$^{-kx}$$ for some k$$ \u003e 0$$

Question 8

What is the amplitude of the function shown in the seventh image?

Accepted Answer

$$2$$

Question 9

Which of the following is a possible formula for the function in the eighth image?

Accepted Answer

$$y = x^3$ + 2x^2$ - x - 2$$

Question 10

The graph in the ninth image is best described by which equation?

Accepted Answer

$$y = x^2$ - 4$$

Question 11

What is the period of the function $$y = 5 \sin\left(\frac{1}{3}x\right) as $$shown in the sixteenth image?

Accepted Answer

$$6\pi$$

Question 12

In the Fahrenheit vs. Celsius graph (seventeenth image), what is the slope of the line?

Accepted Answer

$$1.8$$

Question 13

For the apple orchard yield graph (fifteenth image), what does the vertical intercept represent?

Accepted Answer

The yield when no fertilizer is used

Question 14

For 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 15

Given the function $$g(x) = \frac{x^2$ - 4}{x^2$ + x}$$, where are the vertical asymptotes?

Accepted Answer

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

Question 16

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

Accepted Answer

$$1$$

Question 17

If a culture of 100 bacteria doubles every 2 hours, how long will it take to reach 3,200 bacteria?

Accepted Answer

$$10$$ hours

Question 18

What is the doubling time for prices increasing at 5% per year?

Accepted Answer

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

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

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