What three things can describe an irrational number?
pi
decimal with three dots
imperfect square root
what is meant by “like terms”?
same variable, same exponent
tell how to find the domain and range of a relation and how to determine whether it is a function
domain is all x’s
range is all y’s
x’s cannot repeat in a function
how does one tell if an equation has one answer, infinitely many answers, or no answer?
one answer —> x=3
infinitely many —-> 0=0
no answer —–> 3=0
describe what happens when we divide an inequality by a negative number on each side?
the inequality sign flips
describe rules in the order of operations
- parenthesis or other grouping symbols
- exponents
- multiply/ divide left to right
- add/ subtract left to right
an “and” sentence shows _____
an “or” sentence shows ____
intersection
Union
explain how y=|x-2|+4 is graphed and what the function represents
to the right 2 and up 4, it is an absolute value
define absolute value
distance from zero and is always positive
what does f(x), g(x), h(x), etc represent?
y
in order to have the equation of a line what two things must one have?
point and slope
what is the slope of a vertical line?
undefined
what is the slope of a horizontal line
zero
what is slope-intercept form of a line?
y=mx+b
what is standard form of a line?
ax+by=c
what is point-slope form of the equation of a line?
y-y1 = m(x-X1)
What two words combine compound inequalities?
and/or
tell three ways to describe or show slope
change in x
run
x2-x1
rate of change
slopes of parallel lines have _____ slopes.
perpendicular lines have ____ ____ slopes.
same
negative reciprocal
what does the correlation coefficient “r” tell us?
how accurate the line of best fit is
how do the lines look in a system of two or more equations with infinitely many answers? in a system with no solution?
infinitely many= same line (overlapping)
no solution = paraell
how do we know where to color a linear inequality on a coordinate plane?
less than = below
greater than = above
how do we determine the answer to the system of linear inequalities in the coordinate plane?
where the shading intersects
anything raised to the zero power is equal to _____
one
how can I make a negative exponent a positive exponent?
put it under a 1
how can I multiply powers with the same base?
leave the base, add the exponents
what happens to the exponents when I divide?
subtract
what happens with the exponents when I raise a power to a power?
multiply
describe how to multiply two binomials
- first
- outside
- inside
- last
FOIL
what are the five steps of trial and error?
- multiply first and last terms
- find a factor pair of that product equal to the middle term
- substitute that factor pair for the middle term
- group 1st and 2nd terms & 3rd and 4th terms and do common monomial
- take one of what is common in the parentheses and put remaining numbers outside into the other set of parentheses
give 5 statements to decide what method one would use to factor a polynomial
- try common monomial
- if two perfect squares with a minus in the middle, do difference of squares
- if 3 terms with understood 1 beside squared, do factor pairs
- if 3 terms no understood 1, do trial and error
- if 4 terms, group
discriminant less than zero ___ ____
equals zero ____ ____
greater than zero ___ ___
two imaginary
one real
two real
the process of ridding the radical from the denominator of a fraction is called
rationalizing to denominator
to simplify a rational expression, first one must _____, then state the ______, and then ______ common factors
factor
restrictions
cancel
in an absolute value inequality, less than is what? greater than is what?
less than = and
greater than = or