Questions and Answers
What is the absolute value?
Distance a number is from zero
What type of shape is an absolute value parent graph?
V-shaped
What is the parent function of absolute value?
y = |x|
What are the two different intervals in absolute value on a graph?
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Where do the function intercept with the Y axis or X axis?
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Example problem: y = |x-4| -2: What's the domain and range? Fill in the blank.
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What is the Vertex of y = |x-4| -2?
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With absolute value equations, do we graph one or both functions?
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If the functions intersect (x & y), is there solutions?
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If the equation is equal to a __________________ number, there is no solution.
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In absolute value equations, we always solve for _____?
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In absolute value equations, we always check what?
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Example problem: 6= 2 |x-1| +2. What are the solutions?
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Does the equation |3x+5| -2 = -1 have a solution? If not, why?
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Can absolute value be on both sides of the equation and have solutions or just one side?
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Study Notes
Key Concepts of Absolute Value
- Absolute value denotes the distance of a number from zero on the number line.
- The graph of an absolute value function has a distinctive V-shaped appearance, indicating increasing and decreasing intervals.
Parent Function and Graphing
- The parent function of absolute value is represented by the equation y = |x|.
- Absolute value graphs will exhibit two distinct intervals: one where the function is increasing and one where it is decreasing.
Intercepts and Vertex
- Intercepts are the points where the graph crosses the X-axis or Y-axis.
- For the function y = |x-4| - 2, the vertex is located at the point (4, -2).
Domain and Range
- The domain of the absolute value function is all real numbers.
- For the function y = |x-4| - 2, the range includes values of y that are greater than or equal to -2.
Graphing and Solutions
- When graphing absolute value equations, both the positive and negative functions should be represented.
- Solutions exist if the two functions intersect at points on the graph.
- If an absolute value equation results in a negative number (e.g., |3x+5| - 2 = -1), it indicates no solution due to the nature of absolute values being non-negative.
Problem-Solving and Checking
- Solve for x in absolute value equations, as the variable x is key to finding solutions.
- It is crucial to verify the correctness of numbers in absolute value equations to ensure valid solutions.
Example Solutions
- For the equation 6 = 2 |x-1| + 2, the solutions are x = 3 and x = -1.
- Ensure all potential solutions are realistic and fit within the defined parameters of absolute value equations.
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Description
Explore key concepts of absolute value functions, including their distinctive V-shaped graphs. Understand the parent function, intercepts, domain, and range through various examples. This quiz will test your knowledge on graphing and analyzing absolute value equations.
