Question 1

Given the function $$y = 4 \sin(2x + \frac{\pi}{3}) - 1$$, what is the amplitude of the graph?

Accepted Answer

$$4$$

Question 2

For the function $$y = 3 \cos(\frac{\pi}{2}x) + 2$$, what is the period?

Accepted Answer

$$\frac{2\pi}{\frac{\pi}{2}} = 4$$

Question 3

Which of the following best describes the vertical shift of $$y = -2 \sin(x) + 5$$?

Accepted Answer

Shifted up by 5 units

Question 4

A trigonometric model for daylight hours in a city is $$y = 2 \sin(\frac{2\pi}{12}x - \frac{\pi}{3}) + 12. $$What is the period of this model?

Accepted Answer

$$12$$

Question 5

Given the cosine function $$y = 5 \cos(\frac{\pi}{6}x)$$, what is the value of $$b ($$the coefficient of $$x$$ inside the cosine)?

Accepted Answer

$$\frac{\pi}{6}$$

Question 6

If the minimum value of $$y = A \sin(Bx + C) + D is$$ $$-3$$ and the maximum value is $$5$$, what is the amplitude?

Accepted Answer

$$4$$

Question 7

A model for the population of a bacteria culture is $$P(t) = 8.97e$$^{0.15t}$$. What is the initial population size?

Accepted Answer

$$8.97$$

Question 8

Given the regression line $$y = 2.3401x + 2.9722$$ for log-transformed data, what is the corresponding exponential model?

Accepted Answer

$$y = e$$^{2.9722}$$e^{2.3401x}$

Question 9

The Michaelis-Menten model for enzyme kinetics is $$v = \frac{V_{max}[S]}{K_M + [S]}. $$What happens to $$v as$$ $$[S]$$ becomes very large?

Accepted Answer

$$v$$ approaches $$V_{max}$$

Question 10

Which transformation should be performed so that the Michaelis-Menten equation $$v = \frac{V_{max}[S]}{K_M + [S]}$$ resembles a linear equation?

Accepted Answer

Take the reciprocal of both sides

Question 11

Given the power model $$y = 5.1164x$$^{1.5285}$$, what is the value of the exponent?

Accepted Answer

$$1.5285$$

Question 12

If a trigonometric function has a period of $$6$$, what is the value of $$b in$$ $$y = \sin(bx)$$?

Accepted Answer

$$\frac{2\pi}{6}$$

Question 13

A model for the height of a Ferris wheel seat is $$h(t) = 10 \sin(\frac{\pi}{15}t) + 12. $$What is the maximum height reached?

Accepted Answer

$$22$$

Question 14

Which of the following is the correct formula for the sum of squared errors (SSE) for a model $$f(x)$$ and observed data $$y$$?

Accepted Answer

$$\sum (f(x_i) - y_i)^2$

Question 15

If the SSE for Model A is $$0.002$$ and for Model B is $$0.005$$, which model fits the data better?

Accepted Answer

Model A

Question 16

Given $$y = 2 \sin(\frac{\pi}{4}x - \frac{\pi}{2}) + 3$$, what is the phase shift?

Accepted Answer

$$\frac{\pi}{2} \div \frac{\pi}{4} = 2$$

Question 17

A cosine function $$y = 7 \cos(3x) - 2 is $$used to model temperature fluctuations. What is the midline of the graph?

Accepted Answer

$$y = -2$$

Question 18

If the regression equation for log-transformed data is $$\ln y = 1.5126 + 1.5285 \ln x$$, what is the corresponding power model?

Accepted Answer

$$y = e$$^{1.5126}$$x^{1.5285}$

Study Guide: Trigonometric Functions, Modeling, and Error Analysis

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