Graphing Absolute Value Functions

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•
Mathematics
•
8th - 9th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is an absolute value function?
Back
An absolute value function is a function that contains an algebraic expression within absolute value symbols, which measures the distance of a number from zero on the number line, always resulting in a non-negative output.
2.
FLASHCARD QUESTION
Front
What is the general form of an absolute value function?
Back
The general form is f(x) = a|bx + c| + d, where 'a' affects the vertical stretch or compression, 'b' affects the horizontal stretch or compression, 'c' shifts the graph left or right, and 'd' shifts it up or down.
3.
FLASHCARD QUESTION
Front
How does the value of 'a' affect the graph of an absolute value function?
Back
The value of 'a' determines the vertical stretch or compression of the graph. If 'a' is positive, the graph opens upwards; if 'a' is negative, it opens downwards.
4.
FLASHCARD QUESTION
Front
What does the vertex of an absolute value function represent?
Back
The vertex is the highest or lowest point of the graph, depending on whether it opens upwards or downwards, and it represents the minimum or maximum value of the function.
5.
FLASHCARD QUESTION
Front
How do you find the vertex of the function f(x) = a|bx + c| + d?
Back
The vertex can be found at the point (-c/b, d). This is the point where the function changes direction.
6.
FLASHCARD QUESTION
Front
What is the domain of an absolute value function?
Back
The domain of an absolute value function is all real numbers, expressed as (-∞, ∞).
7.
FLASHCARD QUESTION
Front
What is the range of an absolute value function that opens upwards?
Back
The range is [d, ∞) where 'd' is the y-coordinate of the vertex.
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