Functions
Radical Expressions
Rational Expressions
Complex Numbers
Formulas
100
This test allows us to determine whether a graph represents a function or not.
VLT (vertical line test)
100
Find 81/2 and 81/3
2sqrt(2) and 2
100
Simplify x3/x and explain the rule used.
x2, this rule follows from the fact that when you divide to numbers with the same base and different exponents, you subtract the exponenets.
100
evaluate (-4)1/2 and (-16)1/2
2i and 4i
100
State the Pythagorean Theorem
a2 +b2=c2
200
This letter of the English alphabet most closely resembles the graph of y=|x|
v
200
An even root of a negative number results in what kind of number?
It results in a complex number
200
What is the main goal of rationalizing the denominator?
Often times mathematicians dislike diving by roots, hence they multiply both the top and bottom of a fraction by a particular root to get rid of it.
200
Complete the sentence: "i is a number such that i2 is...."
-1
200
The square root property says:
when x2 =number, sqrt(x2)= + or - sqrt(number)
300
f(x)=sqrt(x) is defined for what values of x
[0, inf)
300
Find 82/3 and 272/3
4 and 9
300
When rationalizing, in what case do we use the formula: A2-B2 = (A+B)(A-B)?
We use this when we see 2 terms on the bottom of the fraction which we would like to rationalize.
300
A quadratic will have 2 complex roots when its determinant is what?
When its determinant is less than 0.
300
State the quadratic formula and its determinant.
400
f(x)=sqrt(x-1000) is defined for what values of x
[1000, inf)
400
Given that the inside of some radical expression is negative, and that the solution to the radical is a real number, what kind of number must the root be?
It must be an odd root (cube root, 5th root, etc.)
400
When solving a radical equation, what must you do for all solutions?
You must plug it back into the original equation to check if the equality holds. (Check solutions)
400
Evaluate i3 + i2 + i
-1
400
Where does the square root in the distance formula come from.
The distance formula is derived using pythagorean theorem. When solving for the hypotenuse of the triangle created between 2 points, you must take the square root.