Algebra Questions

The ranges of the functions y=sin(x) and y=cos(x) are both [−1,1]

The function g is the inverse of f if g(f(x))=x for each x in the domain of f and f(g(x))=x for each x in the domain of g

The graph of y=Asin(kx) has amplitude A and period 2𝜋k

The Pythagorean Identity: sin2(t)+cos2(t)=1

The sine function is a periodic function with period 2𝜋

A linear equation is an equation which can be written so that each term is either a constant or the product of a constant and a single variable whose exponent is 1

Half-angle formula for sine: sin2(x)=1−cos(2x)2

The slope of a vertical line is undefined, and the slope of a horizontal line is zero

A function f is even if, for every x in the domain of f, f(−x)=f(x) and odd otherwise

Double-angle formula for cosine: cos(2x)=cos2(x)−sin2(x)

All trigonometric functions are defined for all angles

A function f is one-to-one if whenever a and b are in the domain of f and a≠b, then f(a)≠f(b)

All trigonometric functions can be written in terms of sine and/or cosine

The graph of y=−f(x) is the graph of y=f(x) reflected about the x-axis, and the graph of y=f(−x) is the graph of y=f(x) reflected about the y-axis

The slope of a line can be calculated as the change in x divided by the change in y

One way to factor a 4th degree polynomial, if possible, is to treat it as a quadratic polynomial in terms of x2 and then factor the resulting quadratic

For positive values of a and b, the graph of f(x+a)+b is the graph of f(x) shifted a units to the right and b units up

Quadratic factors that have at least one real root are called irreducible quadratic factors

The value x=r is a root of the polynomial function f if and only if (x−r) is a factor of the polynomial f.

The graph of cf(dx) is the graph of f(x) stretched vertically by a factor of c for c>1 (or compressed by a factor of c if 0<c<1) and stretched horizontally by a factor of 1d for 0<d<1 (or compressed by a factor of 1d if d>1)