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AP Calculus AB Unit 1A1: Relations, Functions and Graphs — practice questions — page 3

Explore 94 free Unit 1A1: Relations, Functions and Graphs questions in AP Calculus AB Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A1: Relations, Functions and Graphs questions and exercises with answers

Showing questions 61–90 of 94.

If two ordered pairs (a, b) and (c, d) are equal, then:Read the answer and worked solution →If n(A) = p and n(B) = q, then n(A × B) equals:Read the answer and worked solution →A relation R from set A to set B is, by definition:Read the answer and worked solution →If (x + 1, y - 2) = (3, 1), find x and y.Read the answer and worked solution →Let A = {1, 2, 3} and B = {3, 4}. Find n(A × B):Read the answer and worked solution →Let A = {1, 2} and B = {3, 4}. The total number of relations from A to B is:Read the answer and worked solution →If A × B = {(p, q), (p, r), (m, q), (m, r)}, then A and B are:Read the answer and worked solution →The Cartesian product A × A has 9 elements, two of which are (-1, 0) and (0, 1). The set A is:Read the answer and worked solution →A relation R is defined on A = {1, 2, 3, 4, 6} by R = {(a, b): b is exactly divisible by a; a, b ∈ A}. The domain of R is:Read the answer and worked solution →Identify the function h(x) = x^(2/3) + 2x. Which of the following is INCORRECT?Read the answer and worked solution →Let A = {1, 2} and B = {3, 4}. The number of subsets of A × B is:Read the answer and worked solution →R = {(x, x^3) : x is a prime number less than 10} in roster form is:Read the answer and worked solution →Let A = {x, y, z} and B = {1, 2}. The number of relations from A to B is:Read the answer and worked solution →Choose the correct value of $\dfrac{1+\tan^2 A}{1+\cot^2 A}$.Read the answer and worked solution →In a right triangle $ABC$, right-angled at $B$, if $ an A=\frac{4}{3}$, then $ rac{\sin A}{\cos A}$ is equal toRead the answer and worked solution →$\sin^{-1}(\sin x) = x$ holds for $x$ in which interval?Read the answer and worked solution →If the sum of the first $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?Read the answer and worked solution →A point on an object lies below the horizontal level of an observer. The angle formed by the line of sight with the horizontal is called theRead the answer and worked solution →Choose the correct value of $(\sec A+\tan A)(1-\sin A)$.Read the answer and worked solution →Which expression is equal to $\sqrt{\dfrac{1+\sin A}{1-\sin A}}$ for an acute angle $A$?Read the answer and worked solution →Choose the correct value of $9\sec^2 A-9\tan^2 A$.Read the answer and worked solution →Which of the following is true?Read the answer and worked solution →If $\sin A=\frac{1}{3}$ for an acute angle $A$, what is the value of $\cos A$?Read the answer and worked solution →From a standard deck of 52 playing cards, what is the probability of drawing a heart?Read the answer and worked solution →The derivative of $a^x$ for $a>0$ and $a\neq 1$ isRead the answer and worked solution →Which property of conditional probability is correct?Read the answer and worked solution →Using standard limits, evaluate $\lim_{x\to 0}\dfrac{a^x-1}{x}$ for $a>0$.Read the answer and worked solution →Solve for x: (x − 5)/3 = (x − 3)/5Read the answer and worked solution →Which of the following is a linear equation in one variable?Read the answer and worked solution →Solve for t: 5t − 3 = 3t − 5Read the answer and worked solution →

Worked practice questions

If two ordered pairs (a, b) and (c, d) are equal, then:

  1. a + b = c + d
  2. a = d and b = c
  3. a = c and b = d
  4. a × b = c × d
Show answer and solution

Correct answer: C. a = c and b = d

Equality of ordered pairs requires the FIRST elements equal AND the SECOND elements equal. **So (a, b) = (c, d) iff a = c and b = d.**

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If n(A) = p and n(B) = q, then n(A × B) equals:

  1. p + q
  2. |p - q|
  3. p^q
  4. p × q
Show answer and solution

Correct answer: D. p × q

The Cartesian product A × B has pq ordered pairs — for each of the p elements of A you can pair with each of the q elements of B.

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A relation R from set A to set B is, by definition:

  1. An element of A
  2. A subset of A × B
  3. The set A × B itself
  4. A subset of B × A only
Show answer and solution

Correct answer: B. A subset of A × B

A relation from A to B is any subset of A × B. We isolate it by describing a connection between the first and second elements of the ordered pairs.

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More Mathematics topics

Unit 3B: Implicit Differentiation and Inverse FunctionsUnit 3A: Chain Rule and Composite FunctionsUnit 1A3: Function Composition and InversesUnit 1A2: Trigonometric Functions & Inverse TrigUnit 2: Differentiation and Fundamental Derivative RulesUnit 6A: Indefinite Integrals & Fundamental TheoremUnit 1B3: Asymptotic Behavior and Infinite LimitsUnit 1B1: Limit Concepts and Graphical Limits