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=_______