AP Calculus AB Pre Calculus Review Worksheet # 1 Functions Concepts and Skills In this section we are going to review some basic pre calculus topics as the following: • General properties of functions: Domain, Range, Composition, Inverse, and so on. • Special functions and their graphs: absolute value, greatest integer, polynomial, rational, trigonometric, exponential, and logarithmic. Although these topics are not directly tested on the AP exam, reviewing them will reinforce the calculus comprehension.
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AP Calculus ABPre Calculus ReviewWorksheet # 1
Functions
Concepts and SkillsIn this section we are going to review some basic pre calculus topics as thefollowing:
• General properties of functions: Domain, Range, Composition, Inverse, andso on.
• Special functions and their graphs: absolute value, greatest integer,polynomial, rational, trigonometric, exponential, and logarithmic.
Although these topics are not directly tested on the AP exam, reviewing them willreinforce the calculus comprehension.
80 AP Calculus
Chapter SummaryThis chapter has reviewed some important precalculus topics. These topics are r.directly tested on the AP exam; rather, they represent basic principles important in calcu-lus. These include finding the domain, range and inverse of a function; and understand-ing the properties of polynomial and rational functions, trigonometric and inverse trigfunctions, and exponential and logarithmic functions.
For Be students, this chapter also reviewed parametrically defined functions.
Practice ExercisesDirections: Answer these questions without using your calculator.
1. Iff(x) = x3 - 2x - 1, thenf(-2) =
(A) -17 (B) -13 (C) -5 (D) -1 (E) 3
2. The domain off(x) = x2-1 isx + 1
(A) all x:;t 1 (B) "-\allx:;t 1,-1 (C) all x se=-I(D) x~l (E) all reals
3. The domain of g(x) = ..J ~ - 2 isx -x
(A) all x:;t 0, 1 (B) x ~ 2,x:;tO, 1 (C) x~2(D) x~2 (E) x>2
4. If'j'(x) = x3 - 3x2 - 2x + 5 and g(x) = 2, then g(f(x» =
(A) 2x3 - 6x2 - 2x + 10(D) -3 (E) 2
(B) 2X2 - 6x + 1 (C) -6
5. With the functions and choices as in Question 4, which choice is correct forf(g(x»?
6. Iff(x) = x3 +_Ax2+ Bx - 3 and iff(I) = 4 andf(-I) = -6, what is the value of 2A + B?
(A)(E)
12 (B) 8 (C) 0 (D)-2I
It cannot be determined from the given information.
7. Which of the following equations has a graph that is symmetric with respect to theorigin?
x-I(A) y=- (B) y=2~+1 (C) y=x3+2xx
x(D) y=x3+2 (E) y = x3+ 1
8. Let g be a function defined for all reals. Which of the following conditions is notsufficient to guarantee that g has an inverse function?
(A) g(x) = ax + b, a :;t O. {B)(C) g is symmetric to the origin.(E) g is one-to-one.
g is strictly decreasing.(D) g is strictly increasing.
9. Let y = f(x) = sin (arctan x). Then the range offis
Functions 81
(A)
(D)
{YIO<y~l}
{Y 1- ~ <Y< ~}
(B) {YI-l<y<l} (C)
(E) {Y I - ~ ~ Y-~ ~}{YI-l~y~l}
10. Let g(x) = [cos x-II. The maximum value attained by g on the closed interval[0, 2n:] is for x equal to
(A) -1 (B) ° (C) n:2
(D) 2 (E) n:
11. Which of the following functions is not odd?
(A) f(x) = sin x (B) f(x) = sin 2x (C) f(x) =x3 + 1
x(D) f(x) = -2-1
x+(E) f(x) = ifh
12. The roots of the equationf(x) = ° are 1 and -2. The roots off(2x) = ° are
1 1(A) 1 and -2 (B) - and -1 (C) - - and 12 2(D) 2 and-4 (E) -2 and 4