4.4 Absolute Value and Piecewise Functions

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•
Mathematics
•
12th Grade
•
Hard
+1
Standards-aligned
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1.
FLASHCARD QUESTION
Front
What is the definition of absolute value?
Back
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.
Tags
CCSS.6.NS.C.7C
2.
FLASHCARD QUESTION
Front
How do you find the minimum of a piecewise function?
Back
To find the minimum of a piecewise function, evaluate each piece at its defined intervals and compare the values to determine the lowest point.
Tags
CCSS.HSF-IF.C.7B
3.
FLASHCARD QUESTION
Front
What is the vertex of the function f(x) = |x - h| + k?
Back
The vertex of the function is the point (h, k), which represents the minimum point of the graph if k is the lowest value.
Tags
CCSS.HSF-IF.C.7D
4.
FLASHCARD QUESTION
Front
Describe the transformation of the graph of f(x) = |x| when it is changed to f(x) = |x - 3| + 2.
Back
The graph shifts 3 units to the right and 2 units up.
5.
FLASHCARD QUESTION
Front
What is the minimum value of the function y = |x - 4|?
Back
The minimum value is 0, occurring at x = 4.
Tags
CCSS.HSF-IF.C.7D
6.
FLASHCARD QUESTION
Front
How does the graph of y = |x| look?
Back
The graph of y = |x| is a V-shaped graph that opens upwards, with its vertex at the origin (0,0).
Tags
CCSS.HSF-IF.C.7D
7.
FLASHCARD QUESTION
Front
What is the effect of adding a constant to the absolute value function, such as in f(x) = |x| + c?
Back
Adding a constant c shifts the graph vertically by c units. If c is positive, the graph shifts up; if c is negative, it shifts down.
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