Functions & Their Graphs
This type of function has the property that each x value corresponds to exactly one y value.
What is a function?
The highest exponent of a polynomial determines this property, which affects end behavior.
What is the degree?
The function f(x)=ax is called this type of function if a>0 and a cannot=1
What is an exponential function?
This ratio is opposite over adjacent in a right triangle.
What is tangent?
The set of all points equidistant from a fixed point and a fixed line.
What is a parabola?
The set of all possible input values of a function.
What is Domain?
The factor theorem states that x−c is a factor of f(x) if this condition holds.
What is f(c)=0?
The inverse of an exponential function is called this.
What is a logarithmic function?
The Pythagorean identity relates sin2θ+cos2θ=
A circle with center at (h,k) and radius r is described by this equation.
What is (x−h)2+(y−k)2=r2?
For a function f(x), this is defined as f(x−a) and shifts the graph...
What is horizontally?
These numbers indicate where a rational function might have vertical asymptotes.
What are the zeros of the denominator?
Solve for x: log3(x)=4
What is 81
The amplitude of y=3sin(2x) is this value.
What is 3?
What is the equation of a circle on a graph?
(x-f)2+(y-d)2=r2
The graph of y=∣x∣ is an example of a function that exhibits this type of symmetry.
What is symmetry about the y-axis (even function)?
A cubic function with three distinct real roots and 2 imaginary roots must have at least this many turning points.
trick question it cannot exist?
These properties allow logb(MN) to be rewritten as logb(M)+logb(N)
What are the logarithmic product rules?
The angle of a right triangle in standard position whose sine equals sqrt(3)/2
What is pi/3 radians?
What is the equation of a parabola in conic form?
what is (x - h)2 = 4p(y - k)?
If a function f has an inverse f^-1, this must be true about f.
What is it must be one-to-one?
Long division of polynomials yields this in addition to a quotient.
What is remainder?
The function f(x)=e2x can be rewritten in this form using natural logarithm properties.
what is ln(f(x))=2x?
The formula sin(A+B)=sinAcosB+cosAsinB is an example of this type of trigonometric identity.
What is the sum formula?
The line connecting the vertices of a parabola is called this.
What is the axis of symmetry?