24-25 S1 Final Review ( EAAP )
The piecewise linear function f, defined on -4 <= x <= 4, is shown in the graph. The function g is given by g(x) = x+3. Which of the following is the graph of y = f(g(x))
A.
The table gives the number of alternative-fuel vehicles, in thousands, in use in the United States for selected years from 1996 to 2010. The function A defined by A(t)= (4615t-8727)/-0.542t^2+15t+1 is used to model the data, in thousands, for 6≤ t≤ 20 , where t=6 corresponds to 1996. Which of the following could be a plot of the residuals of the model?
A.
The depth of water, in feet, at a certain place in a lake is modeled by a function. The graph of the function is shown for t≥0 , 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?
A. (3,6) only
Which of the following could be a table of inputs and outputs for the rational function r given by r(x)=frac 2x(x+5)^2 ?
A. -431.111
The table gives values for the invertible functions h and k at selected values of x. What is the value of h^(-1)(k(3)) ?
A. 1
The first term of an arithmetic sequence is 5, and the common difference of the sequence is 2. What is the eighth term of the sequence?
A. 19
The rational function f is given by f(x)= x^k(x-1)(x+3)/x^5+2x-5. where k is a positive integer. For which of the following values of k will the graph of f have a horizontal asymptote at y=0
A. 2
Which of the following names a function with a hole in its graph at x=1 and provides correct reasoning related to the hole?
A. The graph of f(x)=x−1x2−1 has a hole at (1, 2) because the values of x−1x2−1 get arbitrarily close to 2 for x-values sufficiently close to 1, but the function is undefined at x=1.
The polynomial function f is given by f(x)=2x3−3x2−23x+12. Which of the following is true about x+3/f(x)?
A. The remainder of x+3f(x) is 0. The quotient of x+3f(x) is a quadratic polynomial that factors into two linear factors involving only real numbers.
The rational function f is given by f(x)= x^k(x-1)(x+3)/x^5+2x-5. where k is a positive integer. For which of the following values of k will the graph of f have a horizontal asymptote at y=0
A. as x increases without bound. h(x) increases without bound, and as x decreases without bound, h(x) deceases without bound
The rational function h is expressed as the quotient of two polynomial functions f and g by h(x)=g(x)f(x) . The function f is given by f(x)=6x3−x2+60x−25 . If the graph of h has a slant asymptote of y=2x−1 , which of the following describes g ?
A. g has a degree 2 with a leading coefficent of 3.
The function f is given by f(x) = x - 3x²+2. In the xy-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?
A. g(x)=x^4 -3x² - 1
An object is moving in a straight line from a starting point. The distance, in meters, from the starting point at selected times, in seconds, is given in the table. If the pattern is consistent, which of the following statements about the rate of change of the rates of change of distance over time is true?
A. The rate of change of the rates of change is 0 meters per second, and the object is neither speeding up nor slowing down.
The function C models temperature, in degrees Celsius, as a function of time t, in hours, for t≥ 0. The function P models electricity usage, in kilowatts, as a function of temperature, in degrees Celsius. Let K be the composition function defined by K(t)=P(C(t)). Which of the following statements is true about function K?
A.K models electricity usage as a function of time.
The table gives values for a function f at selected values of x. Which of the following is a table of values for the function h given by h(x)=f(x-1)+3 ?
C.
The function f is given by f(x)=x2+1, and the function g is given by g(x)=(x-3)x. Which of the following is an expression for f(g(x))?
C. ) x2-6x+9/x2 (+1)
The function f is defined by f (x) = √4 — ² for -2 ≤ x ≤0. Which of the following expressions defines f-¹ (x)?
C. -√4-² for 0≤x≤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?
C. 14,000
The table describes rates of change of a function f for selected intervals of x. The function f is defined for 0 ≤ x ≤ 4. On which of the following intervals is the graph of f concave down.
C. 2 < x < 3
The figure shows the graph of a quartic polynomial function with zeros at A, B, and C. Which of the following statements gives the multiplicity of the zero at C with correct reasoning?
C. 2, because the quartic polynomial function has three real zeros, one of which must have a multiplicity of 2, and the polynomial does not change signs at C.
The general term of a sequence is given by as=51+3(n−10) , where a0 is the initial value. Which of the following expressions also gives the general term of the sequence?
C. 21+3n
The table gives the amount of debt, in dollars, on an individual's credit card for certain months after opening the credit card. Using an exponential regression y=abx to model these data, what is the debt at month 24 predicted by the exponential function model, to the nearest dollar?
C. 42,159
The function f is given by f(x)=x2+2. The function g is the result of a transformation of f and is given by g(x)=x24+2. Which of the following describes the transformation of the graph of f whose image is the graph of g ?
C. A horizontal dilation by a factor of 2
The second term of a sequence is 6, and the fourth term is 24. Of the following, which statement is true?
C. If the sequence is geometric, the fifth term could be 48.
The population of people in a community is decreasing over time. The population can be modeled by the exponential decay function P(t)=20,000(0.92)t, where t is measured in years since 2020.Based on updated data, a new exponential decay function model for the population was constructed. The new model Q(t) is given by Q(t)=20,000((0.9)(0.92))t.Which of the following describes the relationship between model Q and model P?
C. In model Q the new growth factor is 0.9 times as large as the growth factor in model P
The table gives values of the function f for selected values of x. The function g is given by g(x) = x^2. Which of the following gives values of g(f(x)) for x= -1, x=0, and x=1?
C. Outputs = 011
A music agent is planning a series of concerts at local farms around the nation. The agent is building a model to estimate crowd capacity based on different sizes of square fields. Which type of function is most likely to model crowd capacity in this situation?
C. Quadratic
A family needs to buy one shovel and between one and eight plants, inclusive, for their new garden. The cost of the shovel is a dolars, and the cost of one plant is p dollars. The output relues of which of the bolowns give the possible costs for these iterns, in dollars?
C. The arithmetic sequence Csubn = s + pn for 1 ≤ n ≤ 8
Let ƒ be a rational function that is graphed in the æy-plane. Consider and x=7. The multiplicities of the zeros at . The polynomial in the numerator of f has a zero at x=1 and does not have a zero at x=7 polynomial in the denominator of f has zeros at both x=1 and x=7 statements is true?
C. The graph of f has a hole at x=1 and a vertical asymptote at x=7.
The table gives values for a polynomial function g at selected values of x. If a , then g(a)>g(b) for all a and b in the interval 3 . Which of the following could be true about the graph of g on the interval 3 ?
C. The graph of g is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.
The function g is a function of the form g(x)=a⋅bx , where a=0 and b>0 . The function f is given by f(x)=g(x)+4 . Are the output values of f and g proportional over equal length input value intervals?
C. The output values of g only, not f , are proportional over equal-length input-value intervals.
The function f is given by f(x)=(x+3)4. When f is rewritten in the form f(x)=x4+ax3+bx2+cx+d, which of the following values is greatest?
C. c
The function f is not explicitly given. In the xy-plane, the graph of the function g is the result of a sequence of transformations to the graph of f. The graph of g is the result of dilating the graph of f vertically by a factor of 2, then horizontally by a factor of 3, then translating the result up by 7 units, and then left by 11 units.
C. g(x)=2f(3x+11)+7
The table gives the average rates of change for the functions f, g, h, and for certain intervals of x. Which of the functions is best modeled by a piecewise-linear function with two linear segments with different slopes?
C. h
Both nonzero functions f and g are inveritable. The input values of f are times, in hours, and the output values of f are rates, in miles per hour. The input values of g are rates, in miles per hour, and the output values of g are costs, in dollars. For which of the following are the input values costs, in dollars, and the output values times, in hours?
C. y=f^(-1)(g^(-1)
The functions f and g are given by f(x)=x1 and g(x)=x. What is the domain of the function h given by h(x)=f(g(x)) ?
C.All real numbers greater than 0
In the xy -plane, the graph of a rational function f has a vertical asymptote at x=-5. Which of the following could be an expression for f(x) ?
D. ((x-5)(x-3))/(x-3)(x+5)
The function g is given by g(x)=54x+6. Which of the following defines g−1(x)?
D. (5x-6)/4
An object travels along a horizontal line with velocity given by the function υ. The graph of y=v(t) , which consists of four line segments, is shown for 0≤ t≤ 10. On which of the following intervals is the object's velocity decreasing over the entire interval?
D. 0 < t < 3 and 8 < t < 10
The table gives values of the function f for selected values of a. If the function f is linear, what is the value of f(13) ?
D. 34/3
An X -ray machine is used to eliminate germs in certain food processes. The intensity I, in millirads per hour, of X -rays produced by the machine is inversely proportional to the square of the distance d, in meters, from the machine. For a certain machine, the intensity is 26.5 millirads per hour at a distance of 4 meters. Based on this information and using the same machine, what is the intensity, in millirads per hour, at a distance of 3.3 meters?
D. 38.935
The value, in millions of dollars, of transactions processed by an online payment platform is modeled by the function M . The value is expected to increase by 6.1% each quarter of a year. At time t=0 years, 54 million dollars of transactions were processed. If t is measured in years, which of the following is an expression for M(1) ?
D. 54(1.061)^4t
A table of values is given for a data set that can be modeled with y as a function of x. Two function models, linear and exponential, are constructed using regressions. Residual plots for the two regressions are shown. Which of the following statements is true?
D. An exponential model is more appropriate for these data, and Residual Plot 2 corresponds to the exponential regression.
The function f is not explicitly given. The function g is given by g(x) = f(x+1)-f(x). The function h is given byh(x) = g(x+1)-g(x). If h(x) = -6 for all values of a, which of the following statements must be true?
D. Because h is negative and constant, g is decreasing, and the graph of f is concave down.D
The function f is given by f(x)=x^2+3x−5. Which of the following describes f?
D. For any interval of x<−1.5, the function has a negative rate of change, and for any interval of x>−1.5, the function has a positive rate of change.
An open-top box is constructed by cutting squares that are x inches by z inches from the corners of an 11.2-inch by 13.3-inch rectangular piece of cardboard, and then folding the sides of the box up to make walls. The volume of the box is modeled by the function V' given by V(z)=4x^3-49x^2+148.96z e. Which of the following statements is true about the function V" ?
D. The contextual situation restricts the domain of V to 0 the cardboard determines the domain restriction. , and the relative maximum value of V ' on this domain is 133.929. This is because half of the shorter side of the cardboard determines the domain resticton.
For the polynomial function g, the rate of change of gis increasing for x<2 and decreasing for x>2. Which of the following must be true?
D. The graph of g has a point of inflection at x=2 , is concave up for x<2 , and is concave down for x>2.
The functions f and g are given by f(x)=2^x and g(x)=2^x and g(x)=2^x2^a, where a is greater than 0 . Which of the followingdescribes the relationship between the graph of f and the graph of g?
D. The graph of g is a horizontal translation of the graph of f by -a units.
A water tank is leaking water from a crack in its base. The amount of water, in hundreds of gallons, remaining in the tank f hours after the crack formed can be modeled by W , a decreasing function of time t .Which of the following gives a verbal representation of the function W−1 , the inverse function of W ?
D. W^(-1) is a decreasing function of the amount of water in the tank
The polynomial function f is given by f(x)=(x−4)(3x−1)^2 . Which of the following descriptions of f is true?
D. f is a polynomial of degree 3 with a leading coefficient of 9.
The table above shows values for a function at selected values of x. Which of the following statements about f(x) best fits these data?
D. f(x) is best modeled by a quadratic function because the change in the average rates of change over consecutive equal-length input-value intervals is constant.
Which of the following statements is true about the exponential function h given by h(x)=−3⋅4x ?
D. h is always decreasing, and the graph of h is always concave down.
The rate of people entering a subway car on a particular day is modeled by the function R(t) , where R(t)=0.038t3−0.846t2+6.587t+1.428 for 0≤t≤20 . R(t) is measured in people per hour, and t is measured in hours since the subway began service for the day. Based on the model, at what value of t does the rate of people entering the subway car change from increasing to decreasing?
D. t = 5.505
The binomial theorem can be used to expand an expression of the form a+bn. Which of the following is equivalent to x+3y5 ?
D. the longest answer
The graphs give three residual plots for linear, quadratic, and exponential regressions. Which of the following is true about the residual plots for these regressions?
D.The residual plot for the quadratic regression is without pattern, and the residual plots for the linear and exponential regressions show patterns. Therefore, the quadratic model is appropriate.
The figure shows a swimming pool filled with water. A pump is used to remove water from the pool until the pool is empty. When the pump is running, the rate at which the volume of water in the pool decreases is constant. During the first two hours, the pump works slower than usual due to a broken piece. Then the pump stops working. The broken piece is replaced, and the pump works at its usual rate until the pool is completely emptied of water. The entire process of emptying the pool takes six hours. Which of the following graphs could depict this situation, where time, in hours, is the independent variable, and the volume of water in the pool, in gallons, is the dependent variable?
B.
The binomial theorem can be used to expand the polynomial function p , given by p(x)=(x−3)5 .What is the coefficient of the x3 term in the expanded polynomial?
B. (−3)^2×10
The graph of the function y = g(x) is given. Of the following, on which interval is the average rate of change of g least?
B. -1 <= x <= 0
The table gives values of average life expectancy, in years, for a child born in a given year in the United States. A linear regression is used to construct a linear function model L , where t represents the birth year, t=0 is the year 2000, and L(t) represents the life expectancy in years.For what year does the model predict that the life expectancy of a child born in that year will be 83 years?
B. 2051
The table gives the amount of mold, in square micrometers, on a certain food at time t hours. If the amount of mold grows exponentially, what would the amount of mold be, in square micrometers, at time t=3.75 ?
B. 3.728
A builder is trying to find the maximum area that can be bounded by a rectangular region on a certain plot of land. The builder determined four different areas based on the length of one side of the rectangle for four different rectangles. The table gives values of one side of the rectangle, in meters (m), and the corresponding area, in square meters (m2).After noticing that as one side increases, the area values increase and then decrease, the builder used a quadratic regression to produce a function A(x) that models the area based on the constraints.Of the following, what is the maximum value of A(x), to the nearest integer, based on the model?
B. 347
The students in a precalculus class measured each student's height and arm span, in centimeters. The students calculated a linear regression y=a+bx with heights as the input values and arm spans as the output values. The given residual plot has a point labeled P at coordinates (175,23.4). What does point P indicate in the context?
B. Because point . P is above the x-axis, for the student with a height of 175 cm, the model underestimates the actual arm span value by 23.4 cm.
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 T, 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 7a.m. The function D models the same data as function T, after the shift to daylight saving time. If h still represents the number of hours after midnight, which of the following defines D(h) in terms of T?
B. D(h)=T(h-1)
The graph of the polynomial function g is shown. The function f is defined for 0≤x≤3 and is identical to the function g on that interval.How many total local minima and local maxima does the function f have?
B. Four
The graph of the polynomial function y=P(x) is shown. Which of the following could define P(x) ?
B. P(x) = (x-4)^2(x+3)/12
The function f is given by f(x)=3^x . The function g is given by g(x)=f(x))^b, where b is less than 0. Which of the following describes the relationship between the graphs of f and g?
B. The graph of g is a combination of a horizontal dilatation of the graph of f and a reflection over the y-axis.
A regression model S is constructed for a data set. The residuals from the regression áre ploted and labeled. Based on the vertical axis of the residual plot (not shown), point A is located at 1.3 and point B is located at —2.5. Which of the following statements is true about the model and the estimates produced by the model that correspond to A and B ?
B. The model produces an underestimate at A and an overestimate at B. Based on the absolute values of the residuals, there is a greater error in the model with B than with A.
The function f is given by f(x)=−2x7+5x4+6x2−3 .Which of the following correctly describes the end behavior of f as the input values increase without bound?
B. f(x)→−∞ as x→∞
The function f is given by f(x)=5x6−2x3−3f(x)=5x6−2x3−3. Which of the following describes the end behavior of f ?
B. limx→−∞f(x)=∞limx→−∞f(x)=∞ and limx→∞f(x)=∞limx→∞f(x)=∞
The rational function g is given byg(x)=(x+3)(x−1)(x−2)(x2+3x)(x2−4x−5).For what input values of g are the output values of g equal to 0?
B. −1,0, and 5 only
