Podcast
Questions and Answers
What does the equation y=|x| represent?
What does the equation y=|x| represent?
- Quadratic
- Linear
- Exponential
- Absolute value (correct)
What type of function is represented by y=x^2?
What type of function is represented by y=x^2?
Quadratic
What type of function is represented by y=x?
What type of function is represented by y=x?
Linear
What does the equation y=|x|+k represent?
What does the equation y=|x|+k represent?
What does the equation y=|x|-k represent?
What does the equation y=|x|-k represent?
What does the equation y=|x+k| represent?
What does the equation y=|x+k| represent?
What does the equation y=|x-k| represent?
What does the equation y=|x-k| represent?
What does the equation y=|x| represent in terms of shape?
What does the equation y=|x| represent in terms of shape?
What does the equation y=-|x| represent in terms of shape?
What does the equation y=-|x| represent in terms of shape?
Flashcards
y=|x|
y=|x|
Represents the absolute value function, indicating distance from zero.
y=x^2
y=x^2
Represents a quadratic function, forming a parabolic shape.
y=x
y=x
Represents a linear function, forming a straight line.
y=|x|+k
y=|x|+k
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y=|x|-k
y=|x|-k
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y=|x+k|
y=|x+k|
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y=|x-k|
y=|x-k|
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y=|x| shape
y=|x| shape
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y=-|x| shape
y=-|x| shape
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Study Notes
Types of Functions
- Absolute Value Function: Represented as (y = |x|), produces a "V" shape on the graph, symmetrical around the y-axis.
- Quadratic Function: Represented as (y = x^2), forms a parabola that opens upwards, vertex at the origin.
- Linear Function: Represented as (y = x), depicts a straight line with a slope of 1, passing through the origin.
Transformations of Absolute Value Functions
- Vertical Shift Up: For (y = |x| + k), the graph moves up by (k) units.
- Vertical Shift Down: For (y = |x| - k), the graph moves down by (k) units.
- Horizontal Shift Left: For (y = |x + k|), shifts the graph left by (k) units.
- Horizontal Shift Right: For (y = |x - k|), shifts the graph right by (k) units.
Graph Shapes
- "V" Shape: Exists in absolute value functions, represented as (y = |x|).
- "∧" Shape: Exists in inverted absolute value functions, represented as (y = -|x|), creating a downward-opening "V".
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