Quick Study Notes Flashcards
What is a function?
A relation in which each element of the domain is paired with only one element of the range.
What is the vertical line test?
A method to determine if a relation is a function by checking if a vertical line intersects the graph more than once.
What is the general form of a linear function?
f(x) = mx + b or y = mx + b
What are the components of a linear function?
- m (slope) * b (y-intercept)
What is the standard form of a linear function?
0 = Ax + By + C
How do you find the zeros of a function?
Set y to 0 and solve for x.
What is a polynomial function?
A function that can be written in the form f(x) = ax^n + bx^(n-1) + … + dx + e
What is the degree of a polynomial?
The greatest power of the polynomial with one variable.
What happens when the degree of a polynomial function is odd?
There is at least one real zero.
What happens when the degree of a polynomial function is even?
There may be no real zeros.
What is a quadratic function?
A polynomial function of the form f(x) = ax^2 + bx + c
What shape does the graph of a quadratic function take?
A parabola.
What is the vertex of a parabola?
The critical point where the graph changes from increasing to decreasing or vice versa.
What does the discriminant of a quadratic equation indicate?
The type of roots.
What does b^2 - 4ac > 0 indicate?
Two distinct real roots.
What does b^2 - 4ac = 0 indicate?
Exactly one real root.
What does b^2 - 4ac < 0 indicate?
No real roots (two distinct imaginary roots).
What is a rational function?
A function that can be written in the form f(x) = p(x)/q(x) where q(x) ≠ 0.
What is the parent function for all rational functions?
f(x) = 1/x
What happens to the branches of rational functions?
They approach asymptotes.
What is the sum of two functions?
(f + g)(x) = f(x) + g(x)
What is the difference of two functions?
(f - g)(x) = f(x) - g(x)
What is the product of two functions?
(f * g)(x) = f(x) * g(x)
What is the quotient of two functions?
(f/g)(x) = f(x) / g(x), g(x) ≠ 0
