Finals Review Flashcards
how do you determine if an expression is a polynomial?
- no x as an exponent
- no x in a square root
- no x in a denominator
- no non-whole exponents
UNIT ONE
how do you factor a³+b
SOAP formula
(a+b)(a²-ab+b²)
Same sign, Opposite, Always Positive
UNIT ONE
how do you factor a³-b
SOAP formula
(a-b)(a²+ab+b²)
Same sign, Opposite, Always Positive
UNIT ONE
how do you rationalize a denominator with a CUBE ROOT in the denominator?
multiply it by the CUBE ROOT of that number SQUARED!!!
(this is undoing the cube root by cubing the object)
additionally, opposite sign IF ADDITION OR SUBTRACTION
what is the discriminant?
b^2-4ac of a quadratic
tells you what kind of solutions a problem has
>0 2 real solutions
=0 one solution
<0 2 imaginary solutions (no real)
what is the difference quotient?
f(x+h) - f(x)
over h
basically, plug in (x+h) for every x in the function given and evaluate that. then subtract the original function. finally, divide by h.
how do you find the average rate of change of a function from given time intervals?
think of the times given as points on a graph. plug in the times given (x values) into x, to evaluate for their corresponding y values. Then, do y2-y1 over x2-x1, to find slope, or the average change between those two points on the line.
To find velocity of ball at exactly 2 seconds, go from 2 sec to 2.1 sec, then 2 sec to 2.01 sec, then 2.001, and see where the trend goes. If it’s going 15.4, 15.94, 15.994, then it’s going to 16.
how do you know if a line on a graph is a function?
vertical line test!
what does dividing by a negative do to the sign in an equation with an ≥ instead of an =?
it flips the sign! so ≥ becomes ≤, and vice versa
how do you determine if a function is odd, even, or neither?
change the x to a (-x), then evaluate the equation.
if every sign changes, it’s ODD
if no sign changes, it’s EVEN
if some change or something else happens, it’s NEITHER
how do you find the inverse of a function? how do you find the range of a function?
switch x and y values, then solve for y!
or GRAPH IT
how do you know how many real solutions a function has?
if the x has an exponent, that is the degree. that tells you how many solutions there are.
if there’s a fraction exponent… if the numerator is 2, there are 2 real solutions, and if the numerator is 1 or 3, there is one real solution.
what is the discriminant? what is the difference quotient?
the discriminant is b^2-4ac. it tells you what kind of solutions the quadratic has. if it’s positive, there are 2 real. if it equals 0, there is one solution. if it is negative, there are 2 imaginary solutions
the difference quotient is f(x+h) - f(x).
what does i equal?
square root of -1
what does i^2 equal?
-1
