Podcast
Questions and Answers
What is the horizontal asymptote of the function $y = 2^{x} + 3$?
What is the horizontal asymptote of the function $y = 2^{x} + 3$?
The sine law is used to solve all triangles.
The sine law is used to solve all triangles.
False (B)
A geometric sequence has a first term of 3 and a common ratio of 2. What is the 5th term of the sequence?
A geometric sequence has a first term of 3 and a common ratio of 2. What is the 5th term of the sequence?
48
The maximum or minimum value of a quadratic function occurs at its ______.
The maximum or minimum value of a quadratic function occurs at its ______.
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Match the following trigonometric ratios with their correct definitions:
Match the following trigonometric ratios with their correct definitions:
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Which of the following items are permitted in the exam room?
Which of the following items are permitted in the exam room?
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A relation is considered a function if each value of the dependent variable corresponds with only one value of the independent variable
A relation is considered a function if each value of the dependent variable corresponds with only one value of the independent variable
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What is the purpose of the vertical line test?
What is the purpose of the vertical line test?
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The set of all values of the independent variable of a relation is called the ______.
The set of all values of the independent variable of a relation is called the ______.
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What is the inverse of a function?
What is the inverse of a function?
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The factored form of a quadratic expression is often written in the format $a(x-r_1)(x-r_2)$, where $r_1$ and $r_2$ are the ______ of the quadratic.
The factored form of a quadratic expression is often written in the format $a(x-r_1)(x-r_2)$, where $r_1$ and $r_2$ are the ______ of the quadratic.
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Match the following forms of a quadratic functions with their characteristics:
Match the following forms of a quadratic functions with their characteristics:
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What should you do when finding the inverse of a function?
What should you do when finding the inverse of a function?
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Study Notes
Exam Preparation: Functions 11
- Materials Allowed: Pencils (for multiple choice), pens (black or dark blue ink for free response), calculator.
- Materials Prohibited: Electronic devices (cell phones, tablets, etc.), internet access, cameras, food (except bottled water).
- Exam Format: 10 multiple choice, 10 short answer, 7 open-response questions.
Unit 1: Relations and Functions
- Relation: A set of ordered pairs where independent variable values are paired with dependent variable values.
- Function: A relation where each independent variable value corresponds to only one dependent variable value.
- Domain: The set of all possible input values (independent variable).
- Range: The set of all possible output values (dependent variable).
- Vertical Line Test: If a vertical line intersects a graph at more than one point, the graph does not represent a function.
- Function Notation: Using a symbolic representation of a function (e.g., f(x)).
- Parent Functions: Basic functions used to understand transformations. Students should be familiar with the graphs of 5 parent functions.
- Asymptote: A line that a graph approaches but never touches.
Unit 2: Equivalent Algebraic Expressions
- Polynomials: Expressions with variables and constants (addition, subtraction).
- Multiplying Polynomials: Combining terms through multiplication.
- Factoring Polynomials: Breaking down expressions into smaller factors.
- Factoring Quadratics: Techniques for factoring expressions of the form ax2 + bx + c (including special cases like perfect square trinomials and difference of squares).
- Rational Expressions: Expressions containing fractions with polynomials in the numerator and denominator. Proficiency in multiplying, dividing, adding, and subtracting these is required.
Unit 3: Quadratic Functions
- Quadratic Functions: Functions represented as an equation with degree 2 (e.g.: f(x) = ax2 + bx + c).
- Forms: Students need to be comfortable translating between standard, factored, and vertex forms of quadratic equations.
- Domain and Range: Understanding the possible input (x) and output (y) values for quadratic functions.
- Maximum/Minimum Values: Identifying the highest or lowest point on the graph of a parabola.
- Inverse of a Quadratic Function: Finding the inverse function for a quadratic function.
- Operations with Radicals: Manipulating expressions with roots (square roots, cube roots, etc.).
- Zeros of a Quadratic Function: Finding the x-intercepts of the parabola.
- Solving Quadratic Equations: Techniques used to find the values of x that satisfy a quadratic equation.
Unit 4: Exponential Functions
- Laws of Exponents: Rules for manipulating exponents.
- Rational Exponents: Understanding exponents that are fractions (e.g., x1/2).
- Exponential Equations: Equations involving exponential functions (solving).
- Properties of Exponential Functions: Characteristics like exponential growth or decay and how they relate to graphs.
- Exponential Growth/Decay Problems: Applications of exponential functions in real-world scenarios.
- Transformations of Exponential Functions: Understanding how constants modify the graph of a general exponential equation like y = a*bk(x-d)+c.
- Horizontal Asymptotes: Understanding the horizontal lines exponential function approaches.
Unit 5: Trigonometry
- Trigonometric Ratios: Relationships between angles and ratios of sides in a right-angled triangle (sine, cosine, tangent, etc.).
- Trigonometric Equations: Solving equations involving trigonometric functions.
- Sine and Cosine Laws: Rules for finding sides and angles in non-right-angled triangles.
- The Ambiguous Case of the Sine Law: Situations where the Sine Law may produce multiple possible solutions for a triangle.
- Trigonometric Identities: Equations that are true for all possible values of angles.
Unit 6: Properties of Sinusoidal Functions
- Sinusoidal Functions: Graphs characterized by a wave-like pattern.
- Graphs of Sine and Cosine Functions: Understanding standard sine and cosine graphs: Their properties like period, axis of symmetry, and amplitude.
- Transformations of Sinusoidal Graphs: Analyzing how a, k, d, and c affect the graphs of sine and cosine functions (f(x) = a sin(k(x-d) ) + c and transformations).
Unit 7: Sequences and Series
- Arithmetic Sequences: Sequences with a constant difference between consecutive terms. (Calculating common difference, general term, and recursive formulas).
- Geometric Sequences: Sequences with a constant ratio between consecutive terms. (Calculating common ratio, general term, and recursive formulas)
- Arithmetic Series: Sum of terms in an arithmetic sequence.
- Geometric Series: Sum of terms in a geometric sequence.
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Description
Prepare for your Functions 11 exam with this quiz covering relations, functions, and key concepts like domain and range. Test your understanding of function notation and the vertical line test through multiple choice and open-response questions.
