Chapter 3

increasing

A function f is __________ on an interval I if, for any choice of x1 and x2 in I, with x1 < x2, we have f(x1) < f(x2).

vertical

A set of points in the xy-plane is the graph of a function if and only if every __________ line intersects the graph in at most one point.

odd

A(n) __________ function f is one for which f(-x) = -f(x) for every x in the domain of f.

even

A(n) __________ function f is one for which f(-x) = f(x) for every x in the domain of f.

the y-axis

An even function is symmetric with respect to __________.

the graph of the function

If a function is defined by an equation in x and y, then the collection of points (x,y) in the xy-plane that satisfy the equation is called __________.

y

Suppose that the graph of a function f is known. Then the graph of y = f(-x) may be obtained by a reflection about the __________-axis of the graph of the function y = f(x).

horizontal; right

Suppose that the graph of a function f is known. Then the graph of y = f(x-2) may be obtained by a(n) __________ shift of the graph of f to the __________ a distance of 2 units.

x-intercept

The graph of a function y=f(x) can have more than one of which type of intercept.

True

True or False. A function f has a local maximum at c if there is an open interval I containing c such that for all x in I, f(x) is less than or equal to f(c).

True

True or False. A function f is decreasing on an interval I if, for any choice of x1 and x2 in I, with x1 < x2, we have f(x1) > f(x2).

False

True or False. Even functions have graphs that are symmetric with respect to the origin.

False

True or False. Every graph represents a function.

False

True or False. The domain and the range of the reciprocal function are the set of all real numbers.

False

True or False. The graph of a function y=f(x) always crosses the y-axis.

False

True or False. The graph of y = g(3x) is the graph of y = g(x) stretched by a factor of 3.

True

True or False. The y-intercept of the graph of the function y=f(x), whose domain is all real numbers, is f(0).

piecewise or piecewise-defined

When functions re defined by more than one equation, they are called __________ functions.