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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 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the inverse of f(x)=10−5xf(x) = 10 - 5x.

    A.

    f−1(x)=2−x5f^{-1}(x) = 2 - \frac{x}{5}

    B.

    f−1(x)=5x−10f^{-1}(x) = 5x - 10

    C.

    f−1(x)=x−105f^{-1}(x) = \frac{x-10}{5}

    D.

    f−1(x)=10+5xf^{-1}(x) = 10 + 5x

  2. 2.

    Let f(x)=x2f(x) = x^2 and g(x)=3xg(x) = 3x. Find (f∘g)(x)(f \circ g)(x).

    A.

    3x23x^2

    B.

    9x29x^2

    C.

    6x26x^2

    D.

    x2+3xx^2 + 3x

  3. 3.

    If f(x)=x+kf(x) = x + k and f−1(10)=4f^{-1}(10) = 4, find the value of kk.

    A.

    6

    B.

    14

    C.

    -6

    D.

    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 their Characteristics

Subtopic

Graphing Functions and their Characteristics under Functions for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the yy-intercept of the function y=ln⁡(x+e)y = \ln(x+e)?

    A.

    (0,0)(0, 0)

    B.

    (0,e)(0, e)

    C.

    (0,1)(0, 1)

    D.

    (0,ln⁡(1))(0, \ln(1))

  2. 2.

    If f(x)=x2f(x) = x^2, which expression represents the function shifted 11 unit to the left?

    A.

    x2+1x^2 + 1

    B.

    x2−1x^2 - 1

    C.

    (x+1)2(x+1)^2

    D.

    (x−1)2(x-1)^2

  3. 3.

    Find the equation of the axis of symmetry for the quadratic function f(x)=(x−5)(x−1)f(x) = (x-5)(x-1).

    A.

    x=3x = 3

    B.

    x=4x = 4

    C.

    x=2x = 2

    D.

    x=6x = 6

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

Transformations of Graphs

Subtopic

Transformations of Graphs under Functions for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The graph of y=f(x)y = f(x) is transformed to y=f(x)+1y = f(x) + 1. This is a:

    A.

    Vertical translation 1 unit up

    B.

    Horizontal translation 1 unit right

    C.

    Vertical stretch by factor 1

    D.

    Reflection in the xx-axis

  2. 2.

    What is the result of applying y=f(−x)y = f(-x) to a function with a domain of x>0x > 0?

    A.

    The domain becomes x<0x < 0

    B.

    The domain stays x>0x > 0

    C.

    The domain becomes all real numbers

    D.

    The domain becomes y>0y > 0

  3. 3.

    If f(x)=1xf(x) = \frac{1}{x}, which equation represents a translation 3 units down?

    A.

    y=1x−3y = \frac{1}{x} - 3

    B.

    y=1x−3y = \frac{1}{x - 3}

    C.

    y=1x+3y = \frac{1}{x + 3}

    D.

    y=1x+3y = \frac{1}{x} + 3

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

Quadratic Functions

Subtopic

Quadratic Functions under Functions for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If the discriminant is zero, the quadratic equation has:

    A.

    Two distinct real roots

    B.

    One real repeated root

    C.

    No real roots

    D.

    Two imaginary roots

  2. 2.

    What is the value of the coefficient bb in the function f(x)=2x2+7x−1f(x) = 2x^2 + 7x - 1?

    A.

    22

    B.

    77

    C.

    −1-1

    D.

    xx

  3. 3.

    What is the minimum value of the function f(x)=(x−1)2+4f(x) = (x - 1)^2 + 4?

    A.

    11

    B.

    −1-1

    C.

    44

    D.

    −4-4

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

Polynomial Functions (Factor and Remainder Theorems)

Subtopic

Polynomial Functions (Factor and Remainder Theorems) under Functions for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If the polynomial f(x)f(x) satisfies f(5)=0f(5) = 0, then which of the following must be true?

    A.

    (x + 5) is a factor

    B.

    (x - 5) is a factor

    C.

    The remainder when divided by x is 5

    D.

    x = 0 is a root

  2. 2.

    Find kk if P(x)=kx3−2x+1P(x) = kx^3 - 2x + 1 and P(1)=0P(1) = 0.

    A.

    1

    B.

    2

    C.

    -1

    D.

    0

  3. 3.

    Which of the following is a factor of 2x2+5x−32x^2 + 5x - 3?

    A.

    (x - 3)

    B.

    (x + 3)

    C.

    (x - 1)

    D.

    (x + 1)

Download the worksheet for Functions - Polynomial Functions (Factor and Remainder Theorems) to practice offline. It includes additional chapter-level practice questions.

Exponential and Logarithmic Functions

Subtopic

Exponential and Logarithmic Functions under Functions for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What happens to the value of y=e−xy = e^{-x} as xx approaches infinity?

    A.

    yy approaches infinity

    B.

    yy approaches 1

    C.

    yy approaches 0

    D.

    yy approaches -infinity

  2. 2.

    If log⁡x=2\log x = 2, find the value of xx.

    A.

    2

    B.

    20

    C.

    100

    D.

    0.01

  3. 3.

    Evaluate the natural logarithm: ln⁡(1e)\ln \left( \frac{1}{e} \right).

    A.

    1

    B.

    0

    C.

    -1

    D.

    e

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

Rational Functions

Subtopic

Rational Functions under Functions for Grade 11 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the range of the function f(x)=2x+1+5f(x) = \frac{2}{x+1} + 5?

    A.

    y≠5y \neq 5

    B.

    y≠−1y \neq -1

    C.

    y≠2y \neq 2

    D.

    y>5y > 5

  2. 2.

    What is the domain of f(x)=x+2x(x−3)f(x) = \frac{x+2}{x(x-3)}?

    A.

    x≠0x \neq 0 and x≠3x \neq 3

    B.

    x≠−2x \neq -2

    C.

    x≠3x \neq 3

    D.

    x∈Rx \in \mathbb{R}

  3. 3.

    Find the xx-intercept of f(x)=x−0.5x+2f(x) = \frac{x - 0.5}{x+2}.

    A.

    (0.5,0)(0.5, 0)

    B.

    (−0.5,0)(-0.5, 0)

    C.

    (−2,0)(-2, 0)

    D.

    (2,0)(2, 0)

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