##### Precalculus
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#### Complete list of Terms and Definitions for Precalculus

Terms Definitions
Rewrite 1/(a^m). a^(-m)
Rewrite a^(log_a x). x
Special Product Formula:(A-B)(A+B) = A^2-B^2
relation set of ordered pairs
Rewrite a^(m/n). nth root of a^m
domain set of all x values
Rewrite the nth root of a^m? a^(m/n)
Which direction do positive angles rotate? Counter-clockwise
A (positive/negative) slope equates to an upward tilt. Positive
cofactor determinant obtained by deleting the row and column of a given element
gaussian elimination transforming the system's augmented matrix into row echelon form by means of row operations
How many radians are in one degree? pi/180
Rewrite log_b m - log_b n. log_b (m/n)
A quadratic function has a minimum function if the graph opens ____. Up
When plotting points on a graph, (open/closed) dots should be used for values that include the dot. Closed
sequence set whose elements have an order similar to that of the positive integers
eccentricity number that indicates how attenuated a conic section is
Special Product Formula:(A-B)^2 = A^2 - 2AB + B^2
Special Product Formula: (A-B)^2 = A^2 - 2AB + B^2
What is the circumference of a unit circle? 2pi
discrete a function w/ a finite number of elements
even functions function with a graph that is symmetric with respect to the y axis
factorial product of a given integer and all smaller positive integers
periodic function function having a graph that repeats itself identically over and over, left to right
Perfect Square: A^2 + 2AB + B^2 or A^2 - 2AB + B^2 = (A+B)^2 or = (A-B)^2
In log_x a, what must a be? a &gt; 0
a(-x)^y If y is an odd power this is equivalent to ____. -ax^y
Two lines are parallel if their slopes are ____ or both are ____. Equal, vertical
dependent y's or range (b/c the value of y depends on the value of x)
cramer's rule method for solving a linear system of equations using determinants
What is factoring? Factoring is the process by which we reverse expanding. For each set of like terms, find a common factor. Then, combine those factors to find the greatest common factor of the whole expression.
How does one multiply fractions?(i.e. a/b * c/d) Multiply the numerators and denominators straight across.(a*c/b*d)
Special Product Formula: (A+B)^3 = A^3 + 3A^2B + 3AB^2 + B3
How does one multiply fractions? (i.e. a/b * c/d) Multiply the numerators and denominators straight across. (a*c/b*d)
How does one multiply fractions? (i.e. a/b * c/d) Think simple. REALLY simple.
When can trigonometric functions have inverses? When their domain is limited
f - g(x) can be rewritten as ____. f(x) - g(x)
Rewrite log_3 (x+1) = 4 in exponential form. 3^4 = x+1
In which quadrants of the unit circle is sine negative? III and IV
odd function if f(-x)=-f(x) for all x in its domain (its graph is symmetric w/ respect to the origin)
complex numbers numbers that can be written as the sum or difference of a real and imaginary number
How does one add fractions of the same denominator? (i.e. a/b + c/b) Add the numerators! (a+c/b)
How does one add fractions of the same denominator? (i.e. a/b + c/b) (no hint. this is pretty obvious.)
Where is the horizontal asymptote in the graph of a rational function where the degree of the numerator is larger than the degree of the denominator? There is no horizontal asymptote.
What are the three instances in which an angle can be co-terminal? Terminal sides are identical Difference between angles is a multiple of 360 degrees Difference between angles is a multiple of 2pi
focus of a parabola fixed point on the interior of a parabola used in the formal definition of the curve
How does one add fractions of different denominators?(i.e. 2/5 + 3/7) Find a common denominator, and multiply the numerators by said denominator. Then add the numerators and put it over the common denominator.(common denominator = 35.35/5 = 7 and 35/7 = 5, so 2*7 = 14 and 3*5 = 15... SO, 14 + 15 = 29...and our final answer is 29/35!!
How does one divide fractions? (i.e. a/b / c/d) You invert the divisor (the second number), and then multiply! (a/b * d/c)
How does one divide fractions? (i.e. a/b / c/d) They call him Flipper, Flipper, faster than liiiightning...
Rewrite arcsin theta = x to find the value of theta. sin x = theta
On a graph of a polynomial function, the leading coefficient is negative and the polynomial degree is even. How will the graph behave? Both ends will point down.
For what range of x is y positive on the graph of f(x) = sin x? 0 through pi
What if we raising something with an exponent to a new power?(a^m)^n Multiply the old and new powers.a^mn
What if the numerator and the denominator of a fraction are being raised to two different negative powers? a^-n/b^/m The negative powers flip the fraction to its reciprocal, and both powers become positive. a^m/b^n
What is the virtual line test? Any vertical line can touch the graph either once or not at all.
What is the formula for general growth? Define all variables. n(t) = n_0 e^(rt) n = compounding periods t = time n_0 = beginning amount r = rate
What are two ways to solve systems of equations? Substitution and elimination by addition.
What is the relation between division and the inverse of a number? Dividing a number by something is the same as multiplying it by 1 over that number.(i.e. a/b = a*1/b)
What is the definition of absolute value? Absolute value is the distance from a number to zero, so there is an |a| greater than or equal to 0 for every number a. The absolute value of a number is always positive or zero.
What is the degree of a polynomial? The degree of a polynomial is simply the highest power of any of the terms.
What is the formula for continuous compounding? Define all variables. A = Pe^(rt) P = Dollars invested e = Euler's number r = Yearly rate t = Time in years
symmetry w/ respect to the y-axis if a function f is defined so that f(x)=f(-x) for all x in its domain (if (a,b) is on the graph, then (-a,b) is also on the graph -- substituting -x for x in the equation results in an equivalent equation)
What if we are raising a fraction to a negative power?(a/b)^-n The negative power flips the fraction into its reciprocal, and the power then becomes positive.(b/a)^n
What is the intersection of two sets and how is it notated? The intersection of two sets is the set that contains all elements common to both sets. It is the &quot;overlap&quot; section. The notation is shaped like an upside down U, or an arc. (which unfortunately isn't on the keyboard)
If there are logs in both sides of an equation, when do they cancel? When their bases are the same.
What if a number has the exponent 0? Any number raised to the power of zero is then equal to 1.
How do you find the inverse of f(x)? Replace f(x) with x, replace x with y, and solve for y. Replace y with f^-1 (x).
What is a closed interval and how is it notated? A closed interval [a,b] is the set of all numbers between AND INCLUDING a and b themselves.It is obviously notated [a,b].
Given points (X1, Y1) and (X2, Y2) on a plane with a single line running through both of them, what is the equation to find the slope of the line. m = (y2 - y1) / (x2 - x1)
What is the union of two sets and how is it notated? A union is the set that consists of all elements that are in S OR T. Basically, it is the set that contains the entirety of both S and T. The two are joined in union. Like a mathematical marriage. A mathemarriage, if you will.The notation then is shaped like a U. (i.e. A U B)
What is an open interval and how is it notated? An open interval (a,b) is the set of all number between a and b but EXCLUDING the endpoints a and b themselves. It is obviously notated (a,b).
How are f(x) = c + sin x and f(x) = c + cos x translated in relation to c? They are shifted up c units
What if we take the nth root of a^n, if n is EVEN? The nth root of a^n when n is EVEN is equal to |a|.