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Explain the concept of increasing functions.
As x increases, y also increases. The graph rises from left to right.
Explain the concept of decreasing functions.
As x increases, y decreases. The graph falls from left to right.
Explain concave up.
Graph curves upward, rate of change is increasing.
Explain concave down.
Graph curves downward, rate of change is decreasing.
What does a zero of a function represent graphically?
The x-intercept of the function's graph.
How are roots and zeros related?
They are the same thing; different names for the x-intercepts.
Increasing function condition.
If a < b, then f(a) < f(b).
Decreasing function condition.
If a < b, then f(a) > f(b).
How to find zeros of a function?
Solve \(f(x) = 0\).
Define a function.
A relation where each input has exactly one output.
What is the domain of a function?
All possible input values.
What is the range of a function?
All possible output values.
Define an independent variable.
The input that you control or change.
Define a dependent variable.
The output that depends on the input.
What is an increasing function?
A function where output values increase as input values increase.
What is a decreasing function?
A function where output values decrease as input values increase.
Define concavity.
The direction of the curve of a graph (upward or downward).
Define a zero of a function.
Where the function's graph intersects the x-axis.
What are roots of a function?
The values of x where f(x) = 0.