Test

The polynomial function k is given by k(7) = ax* - bz" + 15, where a and b are nonzero real constants. Each of the zeros of k has multiplicity 1. In the zy-plane, an z-intercept of the graph of kis (17.997,0). A zero of kis -0.478 - 0.801. Which of the following statements must be true?

B. -0.478 ÷ 0.801 is a zero of k.

The function f is given by f(z) = 2 sin(4z) + cos(2z). Using the period of f, which of the following is the number of complete cycles of the graph of f in the zy-plane on the interval 0 ≤ 1 ≤ 1000 ?

B. 318

The function f is given by f(x) = 526 - 2x3 - 3. Which of the following describes the end behavior of f? A. Lim *) = -00 and Lim (*) = - ∞0 B. lim x -> neg. infinity f(x)= infinity and lim x-> infinity f(x) = infinity C. lim f(x) = -00 and lim f(x) = 00 D. lim f(x) = 00 and lim f(x) = - 00

B. lim x -> neg. infinity f(x)= infinity and lim x-> infinity f(x) = infinity

The function f is given by f(x) =x^2 + 1, and the function gis given by g(x) = (x-3)/x Which of the following is an expression for f(g(x))?

C. (x^2 - 6x + 9)/ x^2 + 1

What are all values of 0, for 0 < 0 < 27, where 2 sin' 0 = — sin 0?

0, pi, 7pi/6, and 11pi/6

Let x and y be positive constants. Which of the following is equivalent to 2 In x - 3 ln y?

A. ln(x^2/y^3)

The exponential function fis defined by f(x) = ab*, where a and b are positive constants. The table gives values of f(x) at selected values of z. Which of the following statements is true?

D. f demonstrates exponential growth because a > 0 and b > 1.

A complex number is represented by a point in the complex plane. The complex number has the rectangular (3,3). Which of the following is one way to express the complex number using its polar coordinates (г, 0)?

A. (3sqrt2 cos (x/4)) + i (3sqrt2sin(x/4))

The table gives values for the functions f and g at selected values of z. Functions f and g are defined for all real numbers. Let h be the function defined by h(z) - f(g(=)). What is the value of h(0) ? A. -2 B. -1 C. 0 D. 2

A. -2

The function S is given by S(t) = 110,40, where kis a constant. if S(4) = 300,000, what is the value of S(12) ?

A. 175,325 B. 214,772 C. 343,764 D. 357,143

Consider the graph of the polar function r = f(®), where f(®) = 1 + 2 sin 8, in the polar coordinate system for 0 < 0 ≤ 27. Which of the following statements is true about the distance between the point with polar coordinates (f(®), 8) and the origin?

A. The distance is increasing for 0 less than or equal to theta less than or equal to pi/2. because f(theta) is pos. and increasing on the interval.

The function f is defined by f(z) - asin(b(z + c) + d), for constants a, b, c, and d. in the zyplane, the points (2,2) and (4,4) represent a minimum value and a maximum value, respectively, on the graph of f. What are the values of a and d?

A. a=1 and d=3

The function g is given by g(x) = 7 sin(2x): Which of the following is an equivalent form for g(x) ? A. g(x) = 14cosxsinx B. g(x) = (7 cos x) (7 sin x) C. g(x) = 7 cos^2 x - 7 sin^2 x D. g(x) = 7-14sin^2x

A. g(x) = 14cosxsinx

The polynomial function pis given by p(x) = (r + 3) (22 - 2x - 15). Which of the following describes the zeros of p? A. p has exactly two distinct real zeros. B. p has exactly three distinct real zeros. C. p has exactly one distinct real zero and no non real zeros D. p has exactly one distinct real zero and two non-real zeros.

A. p has exactly two distinct real zeros.

The figure shows the graph of a function f. The zero and extrema for fare labeled, and the point of inflection of the graph of f is labeled. Let A, B, C, D, and E represent the z-coordinates at those points. Of the following, on which interval is f increasing nd the graph of f concave down? A. the interval from A to B B. the interval from B to C C. the interval from C to D D. the interval from D to E

A. the interval from A to B

Consider the functions f and g given by f(x) = log10(x - 1) + log10(x + 3) and g(x) = log10(x + 9). In the xyplane, what are all z-coordinates of the points of intersection of the graphs of f and g?

A. x=3 only

At a coastal city, the height of the tide, in feet (fl), is modeled by the function h, defined by h(t) - 6.3 cos (§+) + 7.5 for 0 § * § 12 hours. Based on the model, which of the following is true?

A.The maximum height of the tide is 13.8ft

The function f is given by f(x) = 322 + 2x + 1. The graph of which of the following functions is the image of the graph of f after a vertical dilation of the graph of f by a factor of 2? @ m(z) = 12z? + 4z + 1, because this is a multiplicative transformation of f that results from mutiplying each input value I by 2. ® k(z) = 6z? + 4x + 2, because this is a multiplicative transformation of f that results from multiplying f(z) by 2. © ₽(z) = 3(2 + 2) + 2(2 + 2) + 1, because this is an additive transformation of f that results from adding 2 to each input value 7. • n(z) = 3z? + 2x + 3, because this is an additive transformation of f that results from adding 2 to f(*).

B. k(x) = 6x^2 + 4x + 2, because this is a multiplicative transformation of f that results from multiplying f(x) by 2.

In a certain simulation, the population of a bacteria colony can be modeled using a geometric sequence, where the first day of the simulation is day 1. The population on day 4 was 4,000 bacteria, and the population on day 8 was 49,000 bacteria. What was the population of the colony on day 6 based on the simulation? A. 26,500 B. 26,192 C. 14,000 D. 611

C. 14,000

The figure shows the graph of a trigonometric function f. Which of the following could be an expression for f(x) ?

C. 3sin(2(x- x/4)) - 1

Let f be a sinusoidal function. The graph of y = f(x) is given in the ry-plane. What is the period of f? A. 2 B. 3 C. 4 D. 6

C. 4

Let f be a rational function that is graphed in the zy plane. Consider z = 1 and z = 7. The polynomial in the numerator of f has a zero at x= 1 zeros at x = 1 in the numerator and in the denominator are equal. Wnich of the following statements is true?

C. The graph of f has a hole at x = 1 and a vertical asymptote at x = 7

A polynomial function pis given by p(*) = - xx - 4)(x + 2) What are all intervals on which p(7) ≥ 0? A. [-2, 4] B. [-2, 0] U [4, infinity] C. (-infinity, -4] U [0,2] D. (-infinity, -2] U [0, 4]

D. (-infinity, -2] U [0,4]

In the ry-plane, the graph of a rational function f has a vertical asymptote at I = -5. Which of the following could be an expression for f(x) ?

D. (x-5)(x-3)/(x-3)(x+5)

A physical therapy center has a bicycle that patients use for exercise. The height, in inches (in), of the bicycle pedal above level ground periodically increases and decreases when used. The figure gives the position of the pedal Pat a height of 12 inches above the ground at time t — 0 seconds. The pedal's 8-inch arm defines the circular motion of the pedal. If a patient pedals 1 revolution per second, which of the following could be an expression for h(t), the height, in inches, of the bicycle pedal above level ground at time t seconds? 8-12 sint 12 - 8 sin t © 8 - 12sin(2xt)| 12 - 8 sin(2nt) |

D. 12 - 8sin(2pit)

The functions f and g are defined for all real numbers such that g(I) = f(2( - 4)). Which of the following sequences of transformations maps the graph of f to the graph of g in the same ry-plane? A horizontal dilation of the graph of f by a factor of 2, followed by a horizontal translation of the graph of f by - 8 units ® A horizontal dilation of the graph of f by a factor of 2, followed by a horizontal translation of the graph of f by 8 units © A horizontal dilation of the graph of f by a factor of ½, followed by a horizontal translation of the graph of f by — 4 units ® A horizontal dilation of the graph of f by a factor of ;, followed by a horizontal translation of the graph of f by 4 units

D. A horizontal dilation of the graph of f by a factor of ;, followed by a horizontal translation of the graph of f by 4 units

The figure shows the graph of the polar function = /(P), where /(9) = 4 cos(28), in the polar coordinate system for 0 ≤ 8 ≤ 2%. There are five points labeled A, B, C, D, and E. if the domain of f is restricted to O ≤ 8 ≤ $, the portion of the given graph that remains consists of two pieces. One of those pieces is the portion of the graph in Quadrant I from C to E. Which of the following describes the other remaining piece? * The portion of the graph in Quadrant I from E to B ® The portion of the graph in Quadrant II from E to A © The portion of the graph in Quadrant Ill from E to A The portion of the graph in Quadrant ill from E to D

D. The portion of the graph in Quadrant ill from E to D

The function f is given by f(x) = 9 - 25*. Which of the following is an equivalent form for f(2) ? A. f(x) = 3 x 5(x/2) B. f(x) = 3 x 5(2c) C. f(x)= 9 x 5(x/2) D. f(x) = 9 • 5(2x)

D. f(x) = 9 • 5(2x)

The rate of people entering a subway car on a particular day is modeled by the function R, where R(t) - 0.03€* - 0.8467 + 6.587t + 1.428 for 0 ≤ t ≤ 20. (t) is measured in people per hour, and t is measured in hours since the subway began service for the day. Based on the mode, at what value of t does the rate of people entering the subway car change from Increasing to decresing? A. t=20 B. t=17.056 C. t=13.295 D. t= 5.505

D. t=5.505

The increasing function P gives the number of followers, in thousands, for a new musical group on a social media site. The table gives values of P(e) for selected values of t, in months, since the musical group created their account on this social media site. If a model is constructed to represent these data, which of the following best applies to this situation?

D. y= 20 (2/3)^t