Questions and Answers
What is the domain?
X; Input
What is the range?
Y; Output
When is the domain not 'All Real Numbers'?
When the function has a denominator or a square root.
What is interval notation for a domain?
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What is the domain of h(x)= √3-2x?
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How do you determine if a function is even or odd?
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If every term on the right side of the equation stays the same, the function is even.
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If every term on the right side of the equation changes, the function is odd.
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If some terms stay the same and some change, the function is neither even nor odd.
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What is the difference quotient?
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What is slope?
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What is the slope function?
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Parallel lines have _______ slope.
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Perpendicular lines have _______ slope.
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What is point slope form?
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What is the standard form of a linear equation?
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What is a secant?
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What is a tangent?
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Find the average rate of change of f(x)=x^3 when x1=3 and x2=4.
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What is a vertical shift in function transformation?
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What is a horizontal shift in function transformation?
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What is the equation for reflection across the X-axis?
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What is the equation for reflection across the Y-axis?
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Study Notes
Domain and Range
- Domain refers to the set of all possible input values (x) for a function.
- Range indicates the set of all possible output values (y) resulting from the function.
- The domain typically includes "All Real Numbers" except in certain cases:
- When the function contains a denominator.
- When the function involves a square root.
Interval Notation
- Represents sets of numbers using brackets and parentheses, for example, [-3, ∞).
Function Domain Example
- For the function h(x) = √(3 - 2x):
- The expression inside the square root must be non-negative: 3 - 2x ≥ 0.
- Solving yields: x ≤ 3/2.
Function Symmetry
- To determine if a function is even, odd, or neither:
- Replace x with -x in the equation.
- If all terms remain unchanged, the function is even.
- If all terms change, the function is odd.
- If some terms stay the same, the function is neither even nor odd.
Difference Quotient
- This expression, (f(x+h) - f(x))/h, measures the average rate of change of a function.
Slope Concepts
- Slope is defined as the measure of steepness of a line connecting two distinct points.
- Slope Function formula: (∆y)/(∆x) = (y2 - y1)/(x2 - x1).
Line Characteristics
- Parallel lines have the same slope, indicating they run in the same direction.
- Perpendicular lines have slopes that are either negative or reciprocal of one another.
Forms of Linear Equations
- Point-Slope Form: y - y1 = m(x - x1) where m is the slope and (x1, y1) is a point on the line.
- Standard Form: Ax + By = C, where m = -A/B gives the slope.
Secants and Tangents
- A Secant represents a straight line connecting two points on a curve.
- A Tangent represents a straight line that touches a curve at exactly one point.
Average Rate of Change Example
- For the function f(x) = x³ between x1 = 3 and x2 = 4:
- Calculate f(3) = 27 and f(4) = 64.
- Then, average rate of change = (64 - 27)/(4 - 3) = 37.
Function Transformations
-
Vertical Shift:
- Upward change described by y = f(x) + c.
- Downward change described by y = f(x) - c.
-
Horizontal Shift:
- Leftward change described by y = f(x + c).
- Rightward change described by y = f(x - c).
Reflections
- Reflection across the X-axis represented by y = -f(x).
- Reflection across the Y-axis represented by y = f(-x).
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Description
Test your knowledge of key terms and concepts from Pre-Calculus Chapter 1 with these handy flashcards. Explore important definitions such as domain, range, and interval notation, along with practical examples related to function domains. Enhance your understanding and prepare effectively for your test!
