ap pre cal final!

The table gives values for a polynomial funetion fat selected values of z. Let g(z) = af(bz) + c, where a, b, and c are positive constants. In the ry-plane, the graph of g is constructed by applying three transformations to the graph of f in this order: a horizontal dilation by a factor of 2, a vertical dilation by a factor of 3, and a vertica! translation by 5 units. What is the value of g(-4)?

170

The graph of the function y = 9(2) is given. Of the following, on which interyal is the average rate of change of g least?

3<x<4

The leading term of the polynomial function p is a_nx^nwhere an is a real number and n is a positive integer. The Factors of p include (x - 3). (x - i), and (x - (2 + i)). What is the least possible value of n ?

5

The table gives values of the functions fand g for selected values of x. The pattern of the values of f and g continue, repeating every interval of width 6, for 0≤=<48. The graph of the function g is the result of a sequence of dilations of the graph of the function f. Which of the following could describe those dilations?

A horizontal dilation by a factor of 1/3 and a vertical dilation by a factor of 1/2

During a month in a certain town, the temperature increases and decreases over the course of a day. A graph of the average temperatures during that month for any given day is shown. The data in the graph can be modeled by the function 1, where T(h gives the temperature, in degrees Fahrenheit ("F, at time h hours after midnight. At a certain point in that month, there is an adjustment to clocks for daylight saving time, at which point clocks are adjusted 1 hour forward. For example, 6 a.m. instantly becomes 7 a.m. The function D models the same data as Function T, afer the shift to daylight saving time. 1Th still represents the number of hours after midnight, which of the following defines D(h) in terms ofT?

D(h)=T(h-1)

The rational function is given by r (x) = (2x-3)(x-4)(x-2)/(3x-1)(2x+1)(x-1) and is cquivalent to r(x) = p(x)/q(x), where p and q are polynomial functions. Which of the following statements is true?

The degree of pisequal to the degree of q, and lim x->♾️ r(x)=1/3

Let f be a rational function that is graphed in the zy-planc. Consider a = 1 and a = 7. The polynomial in the umerator of / has a zero at a = 1 and does not have a zero at 2 = 7. The polynomial in the denominator of / ha: cros at both 2 - 1 and 2 = 7. The multiplicities of the zeros at 2 = 1 in the numerator and in the denominato are equal. Which of the following statements is true?

The graph off has a hole at a = 1 and a vertical asymptote at a = 7.

The functions g and fare given by g(x) = 3x^2-2x and f(x)=6x^4+5x^3+3x-5. Which of the following statements is true about the remainder when f(x) is divided by g(x)?

The remander is (7x- 5), so g(x) is not a factor of f(x), and the graph of y=f(x)/g(x) does not have a slant asymptote.

the function g is given by g(x)=x^3-3x^2-18x, and the function h is given by h(x)=x^2-2x-35

all real numbers z where 2≠-3, x≠0,x≠6

the function f is given by f(x)=(x+3)^4. When f is rewritten in the form f(x)=x^4+ax^3+bx^2+cx+d, which of the following values is the greatest?

c

Which of the following functions has a zero at x=3 and has a graph in the xy-plane with a vertical asymptote at x=2 and a hole at x=1?

h(x)= x^2-4x+2/x^2-3x+2

The function f is given by f(x)=3x^2+2x+1. The graph of which the following function is the image of the graph f after a vertical dilation of the graph of f by a factor of 2?

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

The depth of water, in feet, at a certain place in a lake is modeled by a function W. The graph of y = W(t) is shown for 0 ≤ t ≤ 30, where t is the number of days since the first day of a month. What are all intervals of t on which the depth of water is increasing at a decreasing rate?

(3,6) only

The polynomial function & is given by k(z) = ax^4- bx^3+ 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 k is (17.997,0). A zero of k is -0.478 - 0.801i. Which of the following statements must be true?

-0.478 + 0.8012 is a zero of k.

The rational function h is given by h(x) = 2x^5+5x^3-2x^2-13/3x^2-2x+7. Which of the following describes the end behavior of h?

As x increases without bound, h(x) increases without bound, and as decreases without bound, h(x) decreases without bound.

The function f has domain |-2, 2) and range (1, 5). The function g is given by g(x) = - 2f(x+ 3) + 4. What are the domain and range of g?

domain: [-5, - 1], range: [-6, 2]

The polynomial function f is given by f(a) = ax^4+ bx^3+ cx^2+ dx+ k, where a ≠ 0 and b,c, d, and k are constants. Which of the following statements about f is true?

f has either a global maximum or a global minimum, but not both.

The graph of which of the following functions in the ay-plane has at least one 2-intercept, at least one hole, at least one vertical asymptote, and a horizontal asymptote?

f(x)=x^2-4/x^2-x-6

The function f is not explicitly given, In the zy-plane, the graph of the function g is the result of a sequence of transformations to the graph off. The graph of g is the result of dilating the graph off vertically by a factor of then horizontally by a factor of 3, then translating the result up by 7 units, and then left by 11 units. Which of th following defines g in terms of f?

g(x)=2f(x+11/3)+7

The function f is given by f(x) = x^4-3x^2+2. In the ry-plane, the graph of the function g is a vertical translation of the graph of the function f downward by 3 units. Which of the following defines g?

g(x)=x^4-3x^2-1