concepts and vocabulary chapter 2
if f(x)=x+1 and g(x)=x^3, then ____=x^3-(x+1)
(g-f)(x)
t/f a function can have more than one y-intercept
f
if the point (5,-3) is a point on the graph of f, the f( )= ____
5,-3
if the domain of f is all real numbers in the interval [0,7] and the domain of g is all real numbers in the interval [-2,5], the domain of f+g is all real numbers in the interval ______
[0,5]
find a so that the point (-1,2) is on the graph of f(x)=ax^2+4
a=-2
the domain of f/g consists of numbers x for which g(x) ____ 0 that are in the domains of both ____ and ___
cannot equal,f,g
an _____ function f is one for which f(-x)=f(x) for every x in the domain of f: an ____ function f is one for which f(-x)=-f(x) for every x in the domain of f
even, odd
t/f even functions have graphs that are symmetric with respect to the origin
f
t/f every relation is a function
f
t/f if no domain is specified for a function f, then the domain of f is taken to be a set of real numbers
f
t/f the cube root function is odd and is decreasing on the interval (-infinity, infinity)
f
t/f the domain and the range of the reciprocal function are the set of all real numbers
f
t/f the domain of the function f(x)=x^2-4/x is {x|xcannot= +-2}
f
t/f the graph of a function y=f(x) always crosses the y-axis
f
t/f to obtain the graph of y=f(x+2)-3 shift the graph of y=f(x) horizantally to the right 2 units and vertically down 3 units
f
suppose that the graph of the 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
horizantal, right
a function f is ____ on an open interval I if, for any choice of x1 and x2 in I with x1<x2, we have f(x1)<f(x2)
increasing
if f is a function defined by the equation y=f(x) then x is called the __ variable and y is the ____ variable
independant, dependant
the graph of f(x)=mx+b is decreasing if m is ____ than zero
less
when functions are defined by more than one equation thay are called ____ functions
piecewise-defined
the set of all images of the elements in the domain of a function is called the _____
range
a ____ ____ is used to help us to see the type of relation, if any, that may exist between two variables
scatter diagram
for the graph of the linear function f(x)=mx+b, m is the ____ and b is the ____
slope, y intercept
t/f a function f has a local maximum at c if there is an open interval I containing c so that, for all x in I, f(x)<equal f(c)
t
t/f a function f is decreasing on an open interval I if, for any choice of x1 and x2 in I, with x1<x2 we have f(x1)>f(x2)
t
t/f if y varies directly with x, then y is a linear function of x
t
t/f suppose that the x intercepts of the graph of y=f(x) are -3 and 2. then the x intercepts of the graph of y=2f(x) are -3 and 2
t
t/f the average rate of change of a linear function f(x)=mx+b is the constant m
t
t/f the correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between -1 and 1 inclusive
t
t/f the cube function is odd ad is increasing on the interval (-infinity, infinity)
t
t/f the domain of (f g)(x) consists of the numbers x that are in the domains of both f and g
t
t/f the graph of y=-f(x) is the reflection about the x-axis of the graph of y=f(x)
t
t/f the independant variable is sometimesreffered to as the arguement of the function
t
t/f the y-intercept of the graph of the function y=f(x), whose domain is all real numbers is f(0)
t
a st 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
vertical
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)
y
if x and y are two quantities, then y is directly proportional to x if there is a nonzero number k such that _____
y=kx
suppose that the x intercepts of the graph of y=f(x) are -2,1, and 5. the x intercepts of y=f(x+3) are ___, ___, and ___
-5,-2,2