Questions and Answers
What does the equation y=|x| represent?
What type of function is represented by y=x^2?
Quadratic
What type of function is represented by y=x?
Linear
What does the equation y=|x|+k represent?
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What does the equation y=|x|-k represent?
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What does the equation y=|x+k| represent?
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What does the equation y=|x-k| represent?
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What does the equation y=|x| represent in terms of shape?
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What does the equation y=-|x| represent in terms of 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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Description
This quiz covers different types of functions, including absolute value, quadratic, and linear functions, alongside their respective graph shapes. It also explores transformations of absolute value functions such as vertical and horizontal shifts. Test your understanding of these fundamental mathematical concepts.
