MCR3UP Final Exam - Part A: Functions and Algebra
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Questions and Answers

Which of the following characteristics is used to determine if a given relation is a function?

  • Each input has multiple outputs
  • The domain contains only whole numbers
  • Each input has only one output (correct)
  • The range contains only positive numbers

    • What is the correct way to determine the min/max of a given quadratic function?

  • Using the vertex form of the function (correct)
  • Solving for the discriminant of the function
  • Finding the x-intercepts of the function
  • Evaluating the function at a single point

    • How can you determine whether a given exponential function represents growth or decay?

  • By examining its y-intercept
  • By analyzing its rate of change (correct)
  • By calculating the absolute value of its output
  • By evaluating it at x=0

    • What is the period of the trigonometric function $y = 3 ext{cos}(4x)$?

    <p>$2 ext{π}$</p> Signup and view all the answers

    How do you determine the amplitude of a given trigonometric function?

    <p>By finding the maximum and minimum points of the function</p> Signup and view all the answers

    What is the first step in finding an equivalent expression to a given algebraic expression?

    <p>Factoring out a common term from the expression</p> Signup and view all the answers

    Study Notes

    Determining Functions

    • A function is determined by checking if each input corresponds to exactly one output.

    Quadratic Functions

    • To determine the minimum or maximum of a quadratic function, find the vertex of the parabola.

    Exponential Functions

    • A given exponential function represents growth if the base is greater than 1, and decay if the base is between 0 and 1.

    Trigonometric Functions

    • The period of a trigonometric function $y = A\cos(Bx)$ is $\frac{2\pi}{B}$, where $B$ is the coefficient of $x$.
    • The period of the trigonometric function $y = 3\cos(4x)$ is $\frac{2\pi}{4} = \frac{\pi}{2}$.

    Amplitude of Trigonometric Functions

    • The amplitude of a trigonometric function is the absolute value of the coefficient of the cosine term.

    Simplifying Algebraic Expressions

    • The first step in finding an equivalent expression to a given algebraic expression is to remove any parentheses by applying the distributive property.

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    Description

    Prepare for the MCR3UP final exam with this quiz focusing on functions and algebra. Test your knowledge with 20 multiple choice questions that cover topics such as determining if a relation is a function, finding function inverses, simplifying expressions, solving quadratic functions, and more.

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