MATH 140 January 18, 2007

The Graph of a Function When a function is defined by an equation in x and y, the graph of a function is the set of all points (x,y) in the xy-plane that satisfy the equation. Vertical line test: A set of points in the plane is the graph of a function if and only if every vertical line intersects the graph in at most one point.

Which are functions?

Determining Function Values Let Is the point (3,14) on the graph of this function? If f(x)=2, what is x? Determine the domain of the function, the x-intercepts and the y-intercept.

Is the point (3,14) on the graph of this function?

If f(x)=2, what is x?

Determine the domain of the function, the x-intercepts and the y- intercept.

Properties of Functions Even and Odd Increasing/Decreasing Minimum/Maximum Average rate of change

Even and Odd A function f is even if for every number x in its domain –x is also in the domain and f(-x) = f(x). A function f is odd if for every number x in its domain –x is also in the domain and f(-x)= - f(x).

Increasing and Decreasing A function f is increasing on an open interval I if, for any choice of a and b in I with a < b, we have f(a) < f(b). A function f is decreasing on an open interval I if, for any choice of a and b in I with a < b, we have f(a) < f(b). A function f is constant on an open interval I if, for any choice of a and b f(a) = f(b).

Maximum and Minimum A function f has a local maximum at c if there is an open interval I containing c so that for all we have f(x) < f(c). A function f has a local minimum at c if there is an open interval I containing c so that for all we have f(x) > f(c).

Min/max and inc/dec

Average rate of change

Find the average rate of change