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Questions and Answers
Which of the following characteristics is used to determine if a given relation is a function?
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?
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?
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 $y = 3 ext{cos}(4x)$?
What is the period of the trigonometric function $y = 3 ext{cos}(4x)$?
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How do you determine the amplitude of a given trigonometric function?
How do you determine the amplitude of a given trigonometric function?
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What is the first step in finding an equivalent expression to a given algebraic expression?
What is the first step in finding an equivalent expression to a given algebraic expression?
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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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