Absolute value functions (HSC SSCE Mathematics Extension 1): Flashcards
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What is an absolute value function?
What is an absolute value function?
A function like y = |f(x)| with non-negative outputs.
How is absolute value defined for x < 0?
How is absolute value defined for x < 0?
|x| = -x if x < 0.
What happens when f(x) < 0 in |f(x)|?
What happens when f(x) < 0 in |f(x)|?
|f(x)| = -f(x) for f(x) < 0.
What is the graph behavior of |f(x)|?
What is the graph behavior of |f(x)|?
Flips negative parts of f(x) over the x-axis.
How to graph y = |x - 3|?
How to graph y = |x - 3|?
For x < 3, y = -x + 3; for x ≥ 3, y = x - 3.
What is a critical point in absolute value functions?
What is a critical point in absolute value functions?
A point where f(x) changes sign, causing cusps.
How does |x^2 - 2x + 1| differ from its quadratic form?
How does |x^2 - 2x + 1| differ from its quadratic form?
It changes behavior for x < 1, affecting the range.
Why are absolute value functions important?
Why are absolute value functions important?
They help minimize errors in fields like engineering.
What is the effect of |2x + 1| on its graph?
What is the effect of |2x + 1| on its graph?
Flips parts below x-axis upward.
What do absolute value functions ensure?
What do absolute value functions ensure?
Outputs are always non-negative.