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Functions

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Function Concepts (Domain, Range, Inverse, Composite)

Subtopic

Function Concepts (Domain, Range, Inverse, Composite) under Functions for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If f(x)=x−1f(x) = x - 1 and g(x)=x2g(x) = x^2, which expression represents (f∘g)(x)(f \circ g)(x)?

    A.

    x2−1x^2 - 1

    B.

    (x−1)2(x - 1)^2

    C.

    x2−2x+1x^2 - 2x + 1

    D.

    x2+1x^2 + 1

  2. 2.

    If f(x)=5x+2f(x) = 5x + 2, find the value of f−1(12)f^{-1}(12).

    A.

    2

    B.

    62

    C.

    10

    D.

    2.8

  3. 3.

    Determine the domain of f(x)=42x−8f(x) = \frac{4}{2x - 8}.

    A.

    x≠4x \neq 4

    B.

    x≠8x \neq 8

    C.

    x≠2x \neq 2

    D.

    x>4x > 4

Download the worksheet for Functions - Function Concepts (Domain, Range, Inverse, Composite) to practice offline. It includes additional chapter-level practice questions.

Graphing Functions and Transformations

Subtopic

Graphing Functions and Transformations under Functions for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The graph of y=x2y = x^2 is translated 7 units to the left. The new equation is:

    A.

    y=(x−7)2y = (x-7)^2

    B.

    y=x2+7y = x^2 + 7

    C.

    y=(x+7)2y = (x+7)^2

    D.

    y=x2−7y = x^2 - 7

  2. 2.

    How is y=cos⁡(x)y = \cos(x) transformed to y=3cos⁡(x)y = 3\cos(x)?

    A.

    Vertical stretch factor 3

    B.

    Horizontal stretch factor 3

    C.

    Vertical shift 3 units up

    D.

    Horizontal shift 3 units right

  3. 3.

    A point (k,m)(k, m) is on y=f(x)y = f(x). What point is on y=f(−x)y = f(-x)?

    A.

    (k,−m)(k, -m)

    B.

    (−k,m)(-k, m)

    C.

    (−k,−m)(-k, -m)

    D.

    (m,k)(m, k)

Download the worksheet for Functions - Graphing Functions and Transformations to practice offline. It includes additional chapter-level practice questions.

Properties of Polynomial Functions

Subtopic

Properties of Polynomial Functions under Functions for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Consider a polynomial function f(x)f(x) with an odd degree and a positive leading coefficient. Which of the following describes the end behavior of its graph?

    A.

    As x→∞,f(x)→∞x \to \infty, f(x) \to \infty and as x→−∞,f(x)→−∞x \to -\infty, f(x) \to -\infty

    B.

    As x→∞,f(x)→−∞x \to \infty, f(x) \to -\infty and as x→−∞,f(x)→∞x \to -\infty, f(x) \to \infty

    C.

    As x→∞,f(x)→∞x \to \infty, f(x) \to \infty and as x→−∞,f(x)→∞x \to -\infty, f(x) \to \infty

    D.

    As x→∞,f(x)→−∞x \to \infty, f(x) \to -\infty and as x→−∞,f(x)→−∞x \to -\infty, f(x) \to -\infty

  2. 2.

    A polynomial f(x)f(x) is defined by f(x)=(x+1)(x−3)(x+5)f(x) = (x + 1)(x - 3)(x + 5). What are the zeros of this function?

    A.

    x=1,x=−3,x=5x = 1, x = -3, x = 5

    B.

    x=−1,x=3,x=−5x = -1, x = 3, x = -5

    C.

    x=1,x=3,x=5x = 1, x = 3, x = 5

    D.

    x=−1,x=−3,x=−5x = -1, x = -3, x = -5

  3. 3.

    According to the Remainder Theorem, what is the remainder when P(x)=x3−2x2+4P(x) = x^3 - 2x^2 + 4 is divided by (x−2)(x - 2)?

    A.

    00

    B.

    22

    C.

    44

    D.

    88

Download the worksheet for Functions - Properties of Polynomial Functions to practice offline. It includes additional chapter-level practice questions.

Properties of Exponential and Logarithmic Functions

Subtopic

Properties of Exponential and Logarithmic Functions under Functions for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the value of log⁡5(5)\log_{5}(\sqrt{5})?

    A.

    1

    B.

    2

    C.

    0.5

    D.

    5

  2. 2.

    Identify the horizontal asymptote of f(x)=2x−10f(x) = 2^{x} - 10.

    A.

    y=10y = 10

    B.

    y=0y = 0

    C.

    y=−10y = -10

    D.

    x=10x = 10

  3. 3.

    What is the range of f(x)=log⁡10(x)+4f(x) = \log_{10}(x) + 4?

    A.

    y>4y > 4

    B.

    All real numbers yy

    C.

    y>0y > 0

    D.

    y≠4y \neq 4

Download the worksheet for Functions - Properties of Exponential and Logarithmic Functions to practice offline. It includes additional chapter-level practice questions.

Properties of Rational Functions

Subtopic

Properties of Rational Functions under Functions for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What are the xx-intercepts of f(x)=x2−25xf(x) = \frac{x^2 - 25}{x}?

    A.

    x=0x = 0

    B.

    x=5x = 5

    C.

    x=5x = 5 and x=−5x = -5

    D.

    x=25x = 25

  2. 2.

    Find the yy-intercept of the function f(x)=x2−93f(x) = \frac{x^2 - 9}{3}.

    A.

    (0,−3)(0, -3)

    B.

    (0,3)(0, 3)

    C.

    (0,−9)(0, -9)

    D.

    (0,0)(0, 0)

  3. 3.

    Find the vertical asymptotes of f(x)=1x2−100f(x) = \frac{1}{x^2 - 100}.

    A.

    x=100x = 100

    B.

    x=10x = 10

    C.

    x=10x = 10 and x=−10x = -10

    D.

    x=0x = 0

Download the worksheet for Functions - Properties of Rational Functions to practice offline. It includes additional chapter-level practice questions.

Solving Equations and Inequalities

Subtopic

Solving Equations and Inequalities under Functions for Grade 12 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Solve the equation log⁡x(16)=2\log_x(16) = 2.

    A.

    x=8x = 8

    B.

    x=4x = 4

    C.

    x=32x = 32

    D.

    x=256x = 256

  2. 2.

    If f(x)=x−4f(x) = x - 4, solve f(f(x))=0f(f(x)) = 0.

    A.

    x=4x = 4

    B.

    x=0x = 0

    C.

    x=8x = 8

    D.

    x=−4x = -4

  3. 3.

    Solve ∣x+3∣=10|x + 3| = 10.

    A.

    x=7,−13x = 7, -13

    B.

    x=7x = 7

    C.

    x=−7,13x = -7, 13

    D.

    x=13x = 13

Download the worksheet for Functions - Solving Equations and Inequalities to practice offline. It includes additional chapter-level practice questions.

Functions - IB Grade 12 Maths Notes & Revision | Krit.club