Untitled Quiz

Study Notes

Slope (m) can be calculated using the formula: ( m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1} ).
Slopes can be categorized into four types: positive slope, negative slope, zero slope, and undefined slope.
Slope-intercept form of a linear equation is represented as ( y = mx + b ), where m is the slope and b is the y-intercept.
Slope point form is expressed as ( y - y_1 = m(x - x_1) ).

Standard form of a linear equation is ( ax + by = c ), where a, b, and c are constants.
To find the x-intercept from standard form, set y = 0 and solve for x.
To find the y-intercept from standard form, set x = 0 and solve for y.

The equation of a horizontal line can be represented as ( y = b ), which has a constant y-value.
The equation of a vertical line is ( x = a ), which has a constant x-value.

SMOG (Simplified Measure of Gobbledygook) is a formula for assessing reading level, calculated as ( G = \sqrt{W} + 3 ) where W is the number of words with three or more syllables.
A radical function is any function that can be expressed through a radical expression.
An extraneous solution is a solution that does not satisfy the original equation.

A function is defined as a relation where each input in the domain corresponds to exactly one output in the range.
The vertical line test determines if a graph represents a function; a graph is a function if no vertical line intersects it more than once.
Polynomial functions are expressed in the form ( f(x) = a_n x^n + a_{n-1} x^{n-1} + ... + a_1 x + a_0 ), with non-negative integer exponents and real-number coefficients.
Rational functions are defined as ( f(x) = \frac{g(x)}{h(x)} ), where g and h are polynomials and h(x) ≠ 0, with degree of h(x) greater than zero.

The domain of a polynomial function is all real numbers, denoted as ( (-\infty, \infty) ).
The domain of a rational function includes all real numbers except where the denominator h(x) equals zero.
A root function involves an integer n (n ≥ 2); if n is even, its domain is where ( g(x) \geq 0 ); if n is odd, the domain includes all real numbers for which ( g(x) ) is defined.