What is an absolute value function?
Algebra Unit 7 Lesson 1 Practice

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Mathematics
•
10th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
An absolute value function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the non-negative value of x. The graph of an absolute value function has a V shape.
2.
FLASHCARD QUESTION
Front
What does the vertex of an absolute value function represent?
Back
The vertex of an absolute value function represents the minimum or maximum point of the graph, depending on the orientation. It is the point where the graph changes direction.
3.
FLASHCARD QUESTION
Front
How does the graph of y = |x - 3| differ from y = |x|?
Back
The graph of y = |x - 3| is shifted 3 units to the right compared to y = |x|. The vertex of y = |x - 3| is at (3, 0).
4.
FLASHCARD QUESTION
Front
What effect does the coefficient in front of the absolute value have?
Back
The coefficient affects the steepness of the graph. For example, in f(x) = a|x|, if |a| > 1, the graph is steeper; if 0 < |a| < 1, the graph is wider.
5.
FLASHCARD QUESTION
Front
What is the general form of an absolute value function?
Back
The general form of an absolute value function is f(x) = a|bx - h| + k, where (h, k) is the vertex, 'a' affects the direction and steepness, and 'b' affects the horizontal stretch.
6.
FLASHCARD QUESTION
Front
What does it mean for a graph to never cross the x-axis?
Back
A graph that never crosses the x-axis indicates that the function has no real roots. For example, the function f(x) = |x| + 1 is always above the x-axis.
7.
FLASHCARD QUESTION
Front
How do you determine the vertex of the function f(x) = |x + 4| - 3?
Back
The vertex of f(x) = |x + 4| - 3 is at the point (-4, -3). This is found by setting the expression inside the absolute value to zero.
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