MTH 160 Unit 2
horizontal, one-to-one
A function f has an inverse that is a function if there is no ___________________ line that intersects the graph of f at more than one point. Such a function is called a/an ________________ function
zero
We exclude from a function's domain real numbers that cause division by
the same
if two nonvertical lines are parallel, then they have ______________________ slope
divisor, quotient, remainder, dividend
After performing polynomial long division, the answer may be checked by multiplying the ____________ by the _______________ and then adding the _____________. This should give the _____________
-5, 1/5
Consider the line whose equation is 5 x plus y minus 2 equals 5x+y−2=0. The slope of any line that is parallel to this line is _______. The slope of any line that is perpendicular to this line is _______.
x, x
If the function g is the inverse of the function f, then f(g(x))=__________ and g(f(x))=___________
f(x2)-f(x1)/x2-x1
Rate of change of (x1, f(x1)) and (x2, f(x2)) is
a negative number
Real numbers that result in a square root of _______ are excluded from a function's domain.
horizontal, to the right
Suppose that the graph of a function f is known. Then the graph of y=f(x−2) may be obtained by a _______ shift of the graph of f _______ a distance of 2 units.
vertical, up
Suppose that the graph of a function g is known. The graph of y=g(x)+2 may be obtained by a _______ shift of the graph of g _______ a distance of 2 units.
x-c
The Factor Theorem states that if f is a polynomial function and f(c)=0, then _________ is a factor of f(x).
f, g(x)
The function left parenthesis (f◦g)(x) is found by replacing each occurrence of x in the equation for _______ with ___________
y=x
The graph of f ^−1 is a reflection of the graph of f about the line whose equation is
0
The slope of a horizontal line is
undefined
The slope of a vertical line is
y, x
The slope of the line through the distinct points left parenthesis x 1 comma y 1 right parenthesisx1, y1 and left parenthesis x 2 comma y 2 right parenthesisx2, y2 can be interpreted as the rate of change in _______ with respect to _______.
(x-h)^2 +(y-k)^2=r^2
The standard form of the equation of a circle with center (h,k) and radius r is _________________
(fg)(x)
f(x)*g(x)
circle, center, radius
The set of all points in a plane that are equidistant from a fixed point is a/an ____________. The fixed point is called the _________. The distance from this fixed point to any point on the geometric figure is called the ____________
composition
The notation f◦g, called the __________________ of the function f with g
standard, parabola, (h,k), a>0, a<0
The quadratic function f(x)=a(x−h)^2+k, a≠0, is in ________ form. The graph of f is called a _______________ whose vertex is the point ________________. The graph opens upward if ____________ and opens downward if _______________
F(a)
The remainder theorem states that if a polynomial F(x) is divided by (x-a), then the remainder R=_______