All Flashcards
What does the graph of an increasing function look like?
The graph rises from left to right.
What does the graph of a decreasing function look like?
The graph falls from left to right.
What does a concave up graph look like?
It curves upward like a bowl.
What does a concave down graph look like?
It curves downward like a frown.
How can you identify zeros on a graph?
Look for points where the graph intersects the x-axis.
How to find zeros of a polynomial?
Set the polynomial equal to zero, factor, and solve for x.
How to determine where a function is increasing or decreasing?
Find the first derivative, find critical points, test intervals.
How to determine where a function is concave up or concave down?
Find the second derivative, find inflection points, test intervals.
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.