Absolute Value Graphs WS

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Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is the definition of an absolute value function?
Back
An absolute value function is a function that outputs the distance of a number from zero on the number line, regardless of direction. It is defined as f(x) = |x|.
2.
FLASHCARD QUESTION
Front
What does the graph of f(x) = |x| look like?
Back
The graph of f(x) = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).
3.
FLASHCARD QUESTION
Front
How does the graph of f(x) = |x - h| + k transform the basic graph of f(x) = |x|?
Back
The graph shifts horizontally by h units and vertically by k units. If h is positive, it shifts right; if negative, left. If k is positive, it shifts up; if negative, down.
4.
FLASHCARD QUESTION
Front
What is the vertex of the function f(x) = |x + 4| + 3?
Back
The vertex is at the point (-4, 3).
5.
FLASHCARD QUESTION
Front
How does the coefficient of x in f(x) = a|x - h| + k affect the graph?
Back
The coefficient 'a' affects the vertical stretch or compression and the direction of the graph. If a > 1, the graph stretches; if 0 < a < 1, it compresses; if a < 0, it reflects over the x-axis.
6.
FLASHCARD QUESTION
Front
What transformation does the equation y = |x| - 7 represent?
Back
The graph of y = |x| - 7 is the graph of y = |x| shifted down 7 units.
7.
FLASHCARD QUESTION
Front
What is the equation of the absolute value function that has a vertex at (3, 4)?
Back
The equation is f(x) = |x - 3| + 4.
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