Roots and Radicals
What is a square root?
The square root of a number is a value that, when multiplied by itself, gives the original number.
What is the definition of a function?
A function is a relation where each input has exactly one output.
What do exponents represent?
Exponents denote repeated multiplication of a base number.
What is a rational function?
A rational function is the ratio of two polynomials.
What is the probability of rolling a 3 on a fair die?
What is 1/6
What constitutes a radical expression?
Radical expressions involve roots, such as square roots, cube roots, etc.
What are the definitions of domain and range?
The domain includes all possible input values, while the range includes all possible output values.
How do logarithms relate to exponents?
Logarithms are the inverse operations of exponentiation.
What causes vertical asymptotes in a rational function?
The vertical asymptotes occur where the denominator is zero and not the numerator.
In probability, what does P(A and B) represent?
What is the intersection of events A and B?
What is the process for simplifying square roots?
To simplify a radical, look for perfect squares and factor them out of the radical.
When is a function considered linear?
A function is linear if it can be expressed in the form y = mx + b.
What is the product rule of logarithms?
The product rule for logarithms states logb(xy) = logb(x) + log_b(y).
How is the horizontal asymptote of a rational function determined?
The horizontal asymptote is determined by the degrees of the numerator and denominator.
What do you call the chance of something happening based on possible outcomes?
What is probability?
What does it mean to rationalize the denominator?
Rationalizing the denominator means eliminating the radical from the bottom of a fraction.
What is the vertical line test?
To determine if a relation is a function, use the vertical line test on its graph.
What is the power rule for exponents?
The power rule for exponents states that (x^m)^n = x^(m*n).
How do you find the zeros of a rational function?
To find the zeros of a rational function, set the numerator equal to zero and solve.
What is the formula for calculating the probability of an event?
What is P(E) = (number of favorable outcomes) / (total number of outcomes)?
How are the roots of a polynomial related to its coefficients?
The product of the roots of a polynomial can often be found using Vieta's formulas.
What is a composite function?
Composite functions involve applying one function to the results of another; if f(x) = x + 2 and g(x) = 3x, find (f ∘ g)(x).
What is the change of base formula?
The change of base formula allows you to convert logarithms to a different base: logb(a) = logk(a)/log_k(b).
What are holes in rational functions?
There can be holes in the graph where a factor cancels out in both the numerator and denominator.
What is the probability of flipping a coin and getting heads three times in a row?
What is (1/2)^3 = 1/8?