PreCalc Chapter 1 Test Flashcards
How can you tell if a function is even? What kind of symmetry does it have?
Plug in -x for x, and your equation will remain exactly the same {{f(x)}}
Reflection symmetry over the y-axis
how do you know if a function is odd? What kind of symmetry does it have?
Plug in -x for x and your equation will be -f(x) (exact opposite). It has rotational symmetry 180 degrees about the origin
if your function is not odd or even, what is it? what kind of symmetry does this kind of function have
neither–no symmetry
what are points of inflection
where concavity changes
which way do you view a graph to tell if it is increasing or decreasing
left to right
what is the difference between intercepts, roots, and zeroes?
no difference
what does an open point signify on a graph
that breaks one of the rules in your piecewise function rules
how would you express that your domain can be all real numbers greater than -2 using interval notation
Domain= {R’s: (-2, [infinity sign])}
what is a secant line
a line that intersects two points
A ________________ is a location on a graph where your line stops increasing and starts decreasing
relative max
The ________ ________ ________ is used to determine whether the graph of an equation is a function of y in terms of x
Vertical Line Test
The _______ of a function f are the values of x for which f(x)=0
zeroes (roots, x-intercepts)
A function f is ______ on an interval when, for any x1 and x2 in the interval, x1 is less than x2 implies f(x1) is greater than f(x2)
decreasing
The ______ ______ _______ _______ between any two points (x1, f(x1)) and (x2, f(x2)) is the slope of the line through the two points, and this lines is called the _____ line
average rate of change, secant
A function f is _____ when, for each x in the domain of f, f(-x)=-f(x)
odd
true or false- a function with a square root cannot have a domain that is the set of all real numbers
false– the x value could be raised to an even root underneath the square root
i.e. y=square root of x^2
if the graph of a function was a) even or b) odd. what ordered pair could also lie on that graph if (-5/3, -7) did
a) (5/3, -7)
b) (5/3, 7)
what is domain
set of all values that the independent variable (usually x) can be
what is the range
the set of all values that the dependent variable (usually y) can be
what does relation mean
set of ordered pairs (mapping, x/y chart, etc.)
what is f(1)=4 in simpler terms?
(1,4) an ordered pair
what is a function
a specific relation saying your x value can never produce two or more y values
true or false– if an equation has a y value which produces 2 x values, it is NOT a function
false- although an x value cannot produce two or more y values, a y value can produce two or more x values
what is a piecewise function
a function with multiple equations, each with designated rules
what is (x^2-1) said to be
difference of perfect squares
what is implied domain
values acceptable for x for a certain function (given)
usually in in piecewise
what is the variable under the radical called
radicand
how do you solve a difference quotient
make two large brackets, plug in when they are asking you to. simplify and solve
how do you express that the domain of a function is x greater than or equal to 1 in interval notation. What notation is it in above?
[-1, infinity) inequality
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 ______.
domain, range, function
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, and the set of all values taken on by the ______ variable is the range
independent, dependent
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 is called the ___________.
implied domain
In calculus, one of the basic definitions is that of a ___________, given f(x+h)-f(x)/h, h cannot =0
difference quotient
What is standard form
Ax+By=C
What is point slope form
y2-y1=m(x2-x1)
what is slope intercept form
y=mx+b
what is slope formula
y2-y1/x2-x1
how would you find the equation of a line parallel to y=3x-7 through (4,1)
your slope is 3, then plug in 4 for x, 1 for y, and 3 for m (in slope intercept) and solve for b.
OR–plug (4,1) in point slope form with m as 3
the simplest mathematical model for relating two variables is the ____ equation in two variables y=mx+b
linear
For a line, the ratio of the change in y to the change in x is called the __ of the line
slope
The _____________ form of the equation of a line with slope m passing through (x1, y1) is y1-y2=m(x2-x1)
point slope
Two lines are ______ iff their slopes are equal
parallel
Two lines are ______ iff their slopes are negative reciprocals of each other
perpendicular
When the x-axis and the y-axis have different units of measure, the slope can be interpreted as a ______
rate
The prediction method __________ is the method used to estimate a point on a line when the point does not lie between the given points
linear extrapolation
Every line has an equation that can be written in __ form
standard
Polynomial functions are _________ and ___________
continuous and curvy
what is the parent function for absolute value?
y=IxI
how do you know if an equation’s graph has x-axis symm? y-axis? origin?
x- plug in negative for y, must be the same
y- plug in negative for x, must be the same
origin- plug in - for both, must be the same
an odd exponent (x^3) signifies what
that the graph will got through each intercept (no repeats)
what is the equation of a circle
(x-h)^2+(y-k)^2=r^2
center (h,k)
radius r
what does { mean?
: ?
set, such that
An ordered pair (a,b) is a ______ of an equation in x and y when the substitutions x=a and y=b result in a true statement
solution
The set of all solution points of an equation is the ___ of the equation
graph
The points at which a graph intersects or touches an axis are called the ______ of the graph
intercepts
A graph is symmetric with respect to the _____if, whenever (x,y) is on the graph, (-x,y) is also on the graph
y-axis
when you construct and use a table to solve a problem, you are using a ______ approach
graphic
what is another name for the coordinate system, where does it come from
cartesian plane, Rene Descarte
distance formula is derived from ______
pythagorean theorem
what are the types of transitions
dilation, reflection, rotation
translation means ____
slide
what is percentage increase (or decrease)
amount increase/original amount
An ordered pair of real numbers can be represented in a plane called the rectangular coordinate system or the ____ plane
cartesian
The point of intersection of the x axis and the y axis is the ________, and the two axes divide the coordinate plane into four parts called ____
origin, quadrants
the ___________ is a result derived from the pythagorean theorem
distance formula
Finding the average values of the representative coordinates of the two endpoints of a line segment in a coordinate plane is also known as using the
midpoint formula
what axis does your independent variable (x) go on? (y)?
x, y
what would the graph x=2 look like?
y=3?
vertical line through 2
horizontal through 3
intercepts are written in
ordered pairs
what is intercept form
x/a + y/b = 1
when a does not equal nor b does not equal 0
how do you determine if an equation represents y as a function of x
set it equal to y–determine if one x value could produce two y values
when writing an equation as a function of another equation, look for
shared variables
when a graph is constant, you always express the ordered pair with _______
brackets [ ]
how do you find average rate of change
F(new x) - F(old x)/new x-old x
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