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Grade 11 · MCR3U · Functions

MCR3U Introduction to Functions Practice Test (with Solutions)

This is where Grade 11 Functions starts: what makes a relation a function, function notation, domain and range, and inverses. On Martian Lab the unit is Functions & Transformations, and the free test has 8 questions, from reading domain and range off four relations in a table to solving f(x) = 1. Work each one out before you open the answer.

Free Functions & Transformations Practice Test

8 questions, exactly as a free account gets them in the first Functions & Transformations test on Martian Lab. Try each one on paper first, then open the answer.

  1. For the following relations, fill in the table.
    ImageDomainRangeSolveIs this relation a function?
    AD =-Find xx if f(x)=1f(x)=1
    BD =R =f(2)=f(2) =
    C-R =f−1(0)=f^{-1}(0) =
    DD =--
    Figure for the question
    Show solution
    ImageDomainRangeSolveIs this relation a function?
    AD = {x∈R, x>−4}\{x \in \mathbb{R},\ x > -4\}-{x∈R, 1≤x≤3}\{x \in \mathbb{R},\ 1 \leq x \leq 3\}Yes
    BD = {x∈R, −4≤x≤5}\{x \in \mathbb{R},\ -4 \leq x \leq 5\}R = {−1,2}\{-1, 2\}f(2)=2f(2) = 2Yes
    C-R = {y∈R, −3≤y≤4}\{y \in \mathbb{R},\ -3 \leq y \leq 4\}f−1(0)=−2,2,or4f^{-1}(0) =-2, 2, or 4Yes
    DD = {1,2,4}\{1, 2, 4\}--No
    Worked solution
  2. State the domain of f(x)=3−x−2f(x) = \dfrac{3}{-x-2}. D = _____
    Show answer
    {χ∈R, χ≠−2}\{\chi \in \mathbb{R},\ \chi \neq -2\}
  3. State the domain of f−1(x)f^{-1}(x), if f(x)=−3(x−9)2−5f(x) = -3(x-9)^2 - 5. D = _____
    Show answer
    Range of f(x)f(x) is {y∈R, y≤−5}\{y \in \mathbb{R},\ y \leq -5\} Therefore, the domain of f−1(x)f^{-1}(x) is {χ∈R, χ≤−5}\{\chi \in \mathbb{R},\ \chi \leq -5\}
  4. Which of the following statements is true?
    1. The graph of a function and that of its inverse are mirror images about the x-axis.
    2. The graph of a function and that of its inverse are mirror images about the y-axis.
    3. The graph of a function and that of its inverse are mirror images about the line y=xy = x.
    4. The graph of a function and that of its inverse are always perpendicular to each other.
    5. The inverse of a function is always a function.
    Show answer
    c) The graph of a function and that of its inverse are mirror images about the line y=xy = x.
  5. Which of the following relations is not a function? I. 2x−1=y22x - 1 = y^{2} II. y=5−xy = \sqrt{5-x} III. y3=xy^{3} = x IV. x2+y=7x^{2} + y = 7 V. y=3x−12y = 3x - \dfrac{1}{2}
    1. I. only
    2. I. and IV
    3. I., III, and IV
    4. II and V
    5. III only
    Show answer
    a) I. only
  6. If f(x)=x2−8f(x) = x^{2} - 8 and g(x)=4x−3g(x) = 4x - 3, find 12f(6)\dfrac{1}{2}f(6).
    Show answer
    12f(6)=12[62−8]\dfrac{1}{2}f(6)=\dfrac{1}{2}[6^{2}-8] =12⋅28=\dfrac{1}{2} \cdot 28 =14=14
  7. If f(x)=x2−8f(x) = x^{2} - 8 and g(x)=4x−3g(x) = 4x - 3, find g(−x+1)g(-x+1).
    Show answer
    g(−x+1)=4(−x+1)−3g(-x+1)=4(-x+1)-3 =−4x+1=-4x+1
  8. If f(x)=x2−8f(x) = x^{2} - 8 and g(x)=4x−3g(x) = 4x - 3, find xx, if f(x)=1f(x) = 1.
    Show answer
    1=x2−81=x^{2}-8 x2−9=0x^{2}-9=0 (x+3)(x−3)=0(x+3)(x-3)=0 x=3x=3 or x=−3x=-3

This Unit on Martian Lab

The lessons go from functions and relations, function notation, domain and range through the basic functions and inverses to transformations.

  1. Functions & Relations
  2. Function Notation, Domain & Range
  3. Basic Functions
  4. Inverse Functions
  5. Transformations
  6. Transformations of Basic Functions

Then 4 full Functions & Transformations practice tests to check yourself.

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Functions & Transformations FAQ

What is on an MCR3U introduction to functions test?+

Telling functions from relations, function notation, domain and range, inverse functions, and transformations of the basic functions. The free questions on this page cover all of it except transformations, which are in the lessons.

How do you tell if a relation is a function?+

Every x has to go to exactly one y. On a graph, use the vertical line test. In a set of ordered pairs, look for a repeated x: {(1, 1), (2, -7), (2, 5), (4, 6)} is not a function because 2 goes to both -7 and 5.

How do you find the domain of an inverse?+

The domain of f⁻¹ is the range of f. For f(x) = -3(x - 9)² - 5 the vertex is a maximum, so the range is y ≤ -5 and the domain of the inverse is x ≤ -5.

What does the graph of an inverse look like?+

The original graph reflected in the line y = x, because the inverse swaps every (x, y) for (y, x). The inverse of a function is not always a function: a parabola's inverse fails the vertical line test unless you restrict the domain.

What does g(-x + 1) mean?+

Substitute -x + 1 everywhere g has an x. With g(x) = 4x - 3, g(-x + 1) = 4(-x + 1) - 3 = -4x + 1.

Functions & Transformations Topics

One idea at a time: a short explanation, then five worked examples.

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