Questions and Answers
What is a linear function?
A linear function changes at a steady constant rate and has a straight non-vertical line graph.
What is the equation of a linear function?
f(x) = mx + b
Which of the following are key terms that relate to linear functions? (Select all that apply)
What is a quadratic function?
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What defines the vertex of a parabola?
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What is the general form of a quadratic equation?
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Which of the following describes features of quadratic functions? (Select all that apply)
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What is an exponential function?
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What is the equation for an exponential function?
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Which terms are associated with exponential functions? (Select all that apply)
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Study Notes
Linear Functions
- Linear Functions change at a steady constant rate, resulting in a straight non-vertical graph.
- The general equation for a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.
- Characteristics include consistent change or growth without acceleration, described with terms like constant, even, and straight line.
- Common applications involve time and distance or speed and distance traveled, illustrating consistent rates of addition or subtraction.
Quadratic Functions
- Quadratic Functions demonstrate non-constant rate changes compared to linear functions, exhibiting a varying rate of change.
- Their graphs form a parabolic curve, which can open upward or downward.
- The vertex of a parabola represents its minimum or maximum point, crucial for determining the function's extremum.
- The standard form of a quadratic equation is f(x) = ax² + bx + c, where a, b, and c are constants.
- Key traits include curvilinear shapes resembling U-shapes and situations involving objects thrown or launched, where gravitational effects are present.
Exponential Functions
- Exponential Functions are characterized by a constant ratio, leading to rapid growth or decay; values increase or decrease quickly.
- The graph of an exponential function displays an upward or downward curve.
- Defined by the equation f(x) = aˣ, where a is a constant base and x is the exponent.
- Key features include doubling or halving values over time, with applications in finance through compound interest and population growth scenarios.
- Also relevant in contexts where substances decrease to half their original amount over time, indicating rapid changes.
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Description
Review key concepts of linear functions with this set of flashcards designed for Pre-AP Algebra 2. Each card explores essential terms, equations, and definitions needed to understand linear functions and their characteristics. Perfect for preparing for tests and solidifying your understanding of this fundamental algebra concept.
