AP Precalculus Unit 1 Flashcards

Flashcards covering key concepts from the AP Precalculus Unit 1 multiple-choice questions, focusing on functions, rates of change, and transformations.

On which open intervals is the graph of f decreasing at an increasing rate?

When the graph of f(x) is decreasing and concave up.

Which interval has the greatest average rate of change of g(x)?

The average rate of change (AROC) is greatest on this interval because it has the largest change in g(x) relative to the change in x.

Describe the behavior of the graph of h(x) from point P to point Q.

The graph of h is increasing and concave up because the rate of change is increasing from point P to Q.

What is the average rate of change of g over the interval 0 ≤ x ≤ 5?

The average rate of change of g over the interval 0 ≤ x ≤ 5 is 1.

For a cubic function f, if the rate of change is positive at x = -4, negative at x = 1, and positive at x = 4, what is true about the graph of f?

The graph of f has one maximum point on the interval (-4, 1) and one minimum point on the interval (1, 4).

If a salesperson earns $400 for the first $10,000 of sales and $200 for each additional $10,000 or partial, what is the commission earned for $75,000 of sales?

The salesperson earns $1,800 in commission.

Which function has two vertical asymptotes, one horizontal asymptote, and no holes?

f(x) = (x-2)²(x-6) / ((x+1)(x-4)²) has two vertical asymptotes, one horizontal asymptote, and no holes.

If the point (2, 4) is on the graph of y = j(x), find a point on the graph of the transformed function y = j(x+2) + 2.

The transformed point on the graph of y = j(x+2) + 2 is (0, 6).

Given g(x) = (5x + 3)² (x-5)'(x − 3) k has end behavior defined by lim g(x) = ∞ and lim g(x) = ∞, which value of k would satisfy the end behavior condition?

k = 6 would satisfy the end behavior condition for the function.

For h(x) = (x² + k) (x − 3)² (x + 5) to have two imaginary roots with integer coefficients, what value(s) of k would satisfy these conditions?

k = 4 would satisfy these conditions, resulting in two imaginary roots.

What is the coefficient of x in the expansion of (2x+5)³?

The coefficient of x in the expansion of (2x+5)³ is 150.

The graph of the polynomial function p is shown above. Which of the following could be an expression for P(x)?

p(x) = -1/2 (x − 1)(x + 2)² (x − 3)

What are all the intervals for which f(x) > 0, Let h(x) = -2x² (x + 2) (x − 3)

(-2,0) and (0,3)

Selected values of the polynomial k are shown in the table above. Which of the following Claim and explanation statements could be true about k(x)?

The graph of k could be concave down because the average rates of change over consecutive equal-length input-value intervals are decreasing.

Let f (x) = (x+4)^3(x-2)^2(x-5)^2 / (x+4)^2(x-5)^3 The graph of ƒ has a zero at which of the following values of x?

x = 2 only

The graph of the function h(x) is shown above. Which of the following statement pairs about h is true?

The rate of change of h is negative and increasing.

The rational function r is given by r(x)= 2x^2-13x+30/x-3 Which of the following statements about r is correct?

graph of r has a slant asymptote of y = 2x + 9.

The graph of the rational function R(x) is shown above. Which of the following could be the expression for R?

R(x) = 2(x+3)(x-1) / ((x-2)(x+3))

Let f (x) = x² + 8x + 4 and g(x) : = 2x²+5x6. Find all intervals on which g(x) ≥ f(x).

(-∞, -2] U [5,∞)

The graphs of the functions f(x) and g(x) are shown above. Which of the following is an expression for g(x) in terms of f(x)?

g(x) = f(2x)

The functions ƒ and g are defined for all real numbers such that g(x) = f(2(x+5)). Which of the following sequences of transformations maps the graph off to the graph of g in the xy-plane?

Horizontal dilation of the graph of ƒ by a factor of 1/2, followed by a horizontal translation of ƒ by 5 units to the left.

What type of function would be the most appropriate to model the relationship between x and y for the data set shown in the table above?

A quadratic function is best, because the rate of change is decreasing at a constant rate.

Let h be a polynomial function whose graph has a point of inflection at x = 4. Which of the following statements about h must be true?

The graph of the rate of change of h has a relative extremum at x = 4.

A nature preserve has 1,400 feet of fencing to enclose a rectangular flamingo habitat. However, one side of the habitat lies along a river and requires no fencing. Express the area of the habitat A as a function of x.

A(x) = x (1,400-x) / 2

The function y = f(x) has a domain of -7≤ x ≤ 12 and a range of -3 ≤ y ≤ 6. The graph of y = g(x) is the result of the transformation g(x) = f(x + 3) − 4. Which of the following gives the domain of g(x)?

-10 ≤ x ≤ 9

Which interval contains two zeros for the rational function m given by: m(x) =(x+3)(x-2)(x+5)(x − 7)² / (x+5)(x-3)²

(-5,10)

Meghan keeps track of her charitable contributions to the local thespian society. The table below shows how her contributions have changed over the past few years. What was the average annual increase between 2019 and 2022?

$142.33

A ball is launched upwards with an initial velocity of 155 feet per second. The distance in feet of the ball from the ground after t seconds is D (t) = 155t - 16t². For what interval of time is the ball more than 278 feet above the ground?

(2.377,7.311)

Let f be the function given by f(x) = 1/8 x4 −x³-3x²+5x

f has global minima of approximately -9.263 and -1.852

The function given by g(x) = (2x 5)(x2-x+3) / (2x-5)(x-2) Has a hole where x = 5/2 Which of the following is lim g(x) ?

27

The rational function R is given by R(x) = 1.92x² + 2.8x - 2.5 / 1.68x²-6.41x + 3.35 At which of the following x-values does the graph of R(x) have a hole?

0.625

The table above provides values of the function f(x) for x-values near x = 3. Which of the following is true for f?

The rate of change of f at x = 3 is approximately 15.

The function V gives the traffic flow in a 24-hour period over the Sunshine Skyway Bridge in Sarasota, Florida. The table above gives the number of vehicles of V(t) for selected values of t, in hours, for 0 ≤t≤ 24. A quartic regression is used to model these data. What is the value of V(19) predicted by the quartic function model?

89.134