68 terms

# Math Vocab Chapter 1

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x-axis
horizontal real number line
y-axis
vertical real number line
origin
point of intersection of vertical and horizontal axis
four regions of coordinate plane
x-coordinate
direct distance from the y-axis
y-coordinate
direct distance from the x-axis
Cartesian plane
an ordered pair of real numbers can be represented in a plane called the rectangular coordinate system
distance formula
a result derived from the Pythagorean Theorem
midpoint formula
finding the average values of the representative coordinates of the two endpoints of a line segment in a Cartesian plane.
solution
an ordered pair that solves an equation when x and y are substituted and the equation is proven true
graph
the set of all solution points of an equation
intercepts
the points at which a graph intersects or touches an axis
y-axis symmetry
when (x,y) is on the graph, (-x,y) is also on the graph
circle; (h,k); r
the equation (x-h)2+(y-k)2=r2 is the standard form of the equation of a ------ with center ---- and radius ---
numerical approach
when you construct and use a table to solve a problem
linear equation
the simplest mathematical model for relation two variable, y=mx+b
slope
for a line, the ratio of the change in y to the change in x
parallel
if & only if slopes are equal
perpendicular
if & only if slopes are negative reciprocals of each other
rate
when the x-axis and the y-axis have different unites of measure, slope can be interpreted as --------.
linear extrapolation
the prediction method used to estimate a point on a line that does not lie between the given points
domain; range; function
a relation that assigns to each element x from a set of inputs, or ------, exactly one element y in a set of outputs, or -------, is called a ------.
verbally; numerically; graphically; algebraically
functions are commonly represented in four different ways
independent variables
for an equation that represents y as a function of x, the set of all values taken on by the ------- variable x is the domain
dependent variables
for an equation that represents y as a function of x, the set of all values taken on by the ----------- variable y is the range.
piecewise-defined function
f(x)= 2x-1 x<0
x2+4 x>=0
implied domain
if the domain of the function f is not given, then the set of values of the independent variable for which the expression is defined
difference quotient
in calculus, one of the basic definitions is given by [f(x+h)-f(x)]/h h cannot equal 0
ordered pairs
the graph of a function is the collection of ------- or (x, f(x)) such that x is the domain of f
Vertical Line Test
used to determine whether the graph of an equation is a function of y in terms of x
zeros
in a function the values of x for which f(x)=0
decreasing
a function f is ------- on an interval if, for any x1 and x2 in the interval, x1 < x2 implies F(x1) > F(x2)
maximum
a function value f(a) is a relative -------- of f if there exists an interval (x1,x2,) containing a such that x1<x<x2 implies f(a)>=f(x)
average rate of change; secant
between any to points (x, f(x)) and (x2, f(x2)) is the slope of the line through the two points, this line is then called the -------- line
odd
a function f is ------- if for the each x in the domain of f, f(-x)=-f(x)
even
a function f is ------- if its graph is symmetric with respect to the y-axis.
f(x)=[IxI]
greatest integer function
f(x)=x
identity function
f(x)=1/x
reciprocal function
f(x)=x2
f(x)= square root of x
square root function
f(x)=c
constant function
f(x)= IxI
absolute value function
f(x)=x3
cubic function
f(x)=ax+b
linear function
rigid transformations
horizontal shifts, vertical shifts, and reflections
nonrigid
transformations that cause a distortion in the shape of the graph of y=f(x)
horizontal shrink; horizontal stretch
a nonrigid transformation of y=f(x) represented by h(x)=f(cx) is a ------------------ if c>1, and a -------------- if 0<c<1
vertical stretch; vertical shrink
a nonrigid transformation of y=f(x) represented by h(x)=cf(x) is a -------------------- if c>1, and a ----------------- if 0<c<1.
Vertical shift C units ^
h(x)=f(x)+c
vertical shift C units down
h(x)=f(x)-c
horizontal shift c units <---
h(x)=f(x+c)
horizontal shift c units --->
h(x)=f(x-c)
two functions f & g can be combined by the arithmetic operations of ---, -------, -----, & ------ to create new functions.
product
the ----- of the function f with g is (f o g)(x)=f(g(x))
inner; outer
to decompose a function look for an --- and an ------- function
inverse
if the composite functions f(g(x))=x and g(f(x))=x then the function f is the ------ function of g
range; domain
the domain of f is the ------ of f-1, and the --------- of f-1 is the range of f
y=x
the graphs of f and f-1 are reflections of each other in the line -----.
one-to-one
a function is ------ if each value of the dependent variable corresponds to exactly one value of the independent variable
Horizontal Line Test
a graphical test for the existence of an inverse function of f
Ax+By+C=0
general form
x=a
vertical line
y=b
horizontal line
y=mx+b
slope-intercept form
y-y1=m(x-x1)
point-slope form
h(x)= -f(x); h(x)=f(-x)
a reflection in the x-axis of y=f(x) is represented by -------, while a reflection in the y-axis of y=f(x) is represented by -----------.
g(x)
the domain of (f o g) is all x in the domain of g such that ------ is in the domain of f.