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Algebra
math 101
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Terms in this set (55)
which of the following represents a function
equation, graph, ordered pairs
which the following does not describe a function
x^2+(y-1)^2=9
the graph of a function y=f(x),whose domain is all real numbers, always crosses the y-axis
true
the x-int of the graph of the function y=f(x),whose domain is all real numbers, is f(0)
false
all relations are functions
false
to find the x-int for the graph of an equation
replace y with zero
a graph is symmetric with respect to the y-axis if for every point (a,b) on the graph, the point ________ is also on the graph
(-a, b)
given that (-3, 1) is a point on a graph of an odd function, what other point is also on the graph?
(3, -1)
which of the following functions has origin symmetry
f(x)=x^3
the function of f(x)=1/x
has a restricted domain
which of the following functions has a domain different than its range
f(x)=|x|
the function f(x)=3x^2 is classified as a
quadratic
if f(x) is an odd function, then the graph is symmetric about _______
the origin
which of the following is an even function
f(x)=|x|
if (x1, y1) and (x2, y2) are points on a line the slope of the line is given by
m= y2-y1/x2-x1
every horizontal line has a slope of
0 (H0Y)
a line with a pos slope always rises to the
right
the equation of a vertical line through the point (-3,4) is
x= -3 (VUX)
the graph of the equation y=4x-5 has the following characteristics:
slope= 4, y-int= -5
the slope of any line perpindicular to y=1-3x is
1/3
one way to graph the line y=-x+3 by hand is to plot
(0,3) then go down 1 and right 1
the slope of any line is
change of y/ change of x
slope intercept form
y=mx+b
the lines y=2x+3 and y=ax+5 are parallel to
a=2
the graph of a quadratic function is a
parabola
the vertex of the parabola, f(x)=2(x-3)^2-5 is:
(3, -5)
to change f(x)=ax^2+bx+c to f(x)=a(x-h)^2+k you have to:
complete the square
the max or min of the parabola occurs at
the vertex
the y-value of the max or min of a quadratic function is
y= f(-b/2a)
the axis of symmetry of a quadratic function is
x= (-b/2a)
the domain of every polynomial function is the set of all real numbers
true
the x-int of the graph of a polynomial function are called turning points
false
if a polynomial f(x) is divided by x-1, then the remainder equals
f(1)
list zeros and multiplicity for f(x)=-1/3(x+2)(x-2)^2
-2 (m1), 2 (m2)
it is possible for a cubic polynomial function to have no real zeros
false
a polynomial function of degree three can have at most _______ non-real zeros
2
the degree of the polynomial f(x)= -2(x+1)^2(x-3)(x-2)^3
6
the domain of the function f(x)= 3/ x+2 is:
all real numbers, such that x cannot equal 2
the x-axis is the horizontal asymptote when
the degree of the denominator is more than the degree of the numerator
the graph of a rational function can have
more than one vertical asymptote
to find the vertical asymptote of a rational function
find the zeros of the denominator
a function of f is one to one if for a and b in its domain and f(a)=f(b) then:
a=b
a function f(x) has an inverse function g(X) if :
f(x) is one to one
given the point (1,3) on the graph of a on not one function F, what point must be on the graph of f^-1
(3,1)
if (4, -1) is on the graph of g(x), then ________
g^-1(-1)=4
if f(x)=3^x, F=f(x+2) is the same a f except it is shifted
2 units to the left
e, an irrational number, is approximately equal to
2.718
logv2(-8)=
doesn't exist
to find the distance between two points (x1, y2) and (x2, y2) in the coordinate plane, use the formula
square root (x2-x1)^2+(y2-y1)^2
to complete the square of the expression x^2-6x, add
9
if the graphs of a system of two linear equations result in parallel lines, the system is:
inconsistent, no solution
the equation in a system of equations is consistent when:
the solution produces 0=0, the lines intersect at one point, the system is dependent
if a system of 2 equations has only one solution, then the lines representing the equation
intersect once
when solving a system of equations by the elimination method, you get a result of 0=5 after adding the equations. this means the system is:
inconsistent, no solution
which of the following os not allowed in matrix row operation?
mutiplying one row by another row
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