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Functions

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

Concept of a function, domain, and range

Subtopic

Concept of a function, domain, and range under Functions for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the domain of f(x)=5x−10f(x) = \frac{5}{x - 10}?

    A.

    All real numbers except 10

    B.

    All real numbers except 5

    C.

    x>10x > 10

    D.

    x<10x < 10

  2. 2.

    Why does a circle not represent a function of yy in terms of xx?

    A.

    It has no domain

    B.

    It fails the vertical line test

    C.

    It is not a straight line

    D.

    It has no range

  3. 3.

    If f(x)=3x−2f(x) = 3x - 2, what is the yy-intercept of the graph of ff?

    A.

    3

    B.

    2

    C.

    -2

    D.

    0

Download the worksheet for Functions - Concept of a function, domain, and range to practice offline. It includes additional chapter-level practice questions.

Function notation and graphing

Subtopic

Function notation and graphing under Functions for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    For the function g(x)=x+4g(x) = \sqrt{x + 4} to be defined as a real number, what is the domain of xx?

    A.

    x>−4x > -4

    B.

    x≥−4x \geq -4

    C.

    x≤4x \leq 4

    D.

    x∈Rx \in \mathbb{R}

  2. 2.

    Determine the range of the function f(x)=x2+1f(x) = x^2 + 1 for all real values of xx.

    A.

    y>0y > 0

    B.

    y≥0y \geq 0

    C.

    y>1y > 1

    D.

    y≥1y \geq 1

  3. 3.

    What is the yy-intercept of the graph of the function f(x)=2x2−5x+3f(x) = 2x^2 - 5x + 3?

    A.

    (0,3)(0, 3)

    B.

    (0,−5)(0, -5)

    C.

    (3,0)(3, 0)

    D.

    (0,2)(0, 2)

Download the worksheet for Functions - Function notation and graphing to practice offline. It includes additional chapter-level practice questions.

Linear, quadratic, exponential, and logarithmic functions

Subtopic

Linear, quadratic, exponential, and logarithmic functions under Functions for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which constant represents the base of natural logarithms?

    A.

    π\pi

    B.

    ii

    C.

    ee

    D.

    ϕ\phi

  2. 2.

    Solve for xx: 2x+5=112x + 5 = 11.

    A.

    3

    B.

    8

    C.

    6

    D.

    4

  3. 3.

    Which of the following is the inverse of the function f(x)=10xf(x) = 10^x?

    A.

    f−1(x)=x10f^{-1}(x) = x^{10}

    B.

    f−1(x)=log⁡10xf^{-1}(x) = \log_{10} x

    C.

    f−1(x)=110xf^{-1}(x) = \frac{1}{10^x}

    D.

    f−1(x)=10xf^{-1}(x) = 10x

Download the worksheet for Functions - Linear, quadratic, exponential, and logarithmic functions to practice offline. It includes additional chapter-level practice questions.

Transformations of graphs (translations, reflections, stretches)

Subtopic

Transformations of graphs (translations, reflections, stretches) under Functions for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    The graph of f(x)=1xf(x) = \frac{1}{x} is transformed into g(x)=1x+2−3g(x) = \frac{1}{x + 2} - 3. What are the translations?

    A.

    Right 2 and Up 3

    B.

    Left 2 and Down 3

    C.

    Left 2 and Up 3

    D.

    Right 2 and Down 3

  2. 2.

    The function f(x)=∣x∣f(x) = |x| is vertically stretched by a scale factor of 0.20.2. What is the resulting equation?

    A.

    g(x)=∣x∣+0.2g(x) = |x| + 0.2

    B.

    g(x)=∣0.2x∣g(x) = |0.2x|

    C.

    g(x)=0.2∣x∣g(x) = 0.2|x|

    D.

    g(x)=∣x−0.2∣g(x) = |x - 0.2|

  3. 3.

    The function f(x)=x3f(x) = x^3 is translated 5 units to the right. What is the equation of the resulting graph?

    A.

    g(x)=(x−5)3g(x) = (x - 5)^3

    B.

    g(x)=x3−5g(x) = x^3 - 5

    C.

    g(x)=(x+5)3g(x) = (x + 5)^3

    D.

    g(x)=x3+5g(x) = x^3 + 5

Download the worksheet for Functions - Transformations of graphs (translations, reflections, stretches) to practice offline. It includes additional chapter-level practice questions.

Composite and inverse functions

Subtopic

Composite and inverse functions under Functions for Grade 10 IB.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If f(x)=x+3f(x) = x + 3, find the value of f−1(f(5))f^{-1}(f(5)).

    A.

    8

    B.

    3

    C.

    5

    D.

    2

  2. 2.

    If f(x)=7xf(x) = 7x, find the value of f(f−1(14))f(f^{-1}(14)).

    A.

    2

    B.

    14

    C.

    98

    D.

    7

  3. 3.

    If f(x)=2xf(x) = \frac{2}{x}, find f−1(1)f^{-1}(1).

    A.

    1

    B.

    2

    C.

    0.5

    D.

    -2

Download the worksheet for Functions - Composite and inverse functions to practice offline. It includes additional chapter-level practice questions.