1.2 & 1.4: Polynomials, Exponential Functions, & Trig

what do each of these values mean ax^n

a: coefficient

x: variable

n: constant integer

What makes a function not a polynomial

if the variable is raised to the power of “not an integer”

What’s a rational function

function divided by a function

what’s the line slope formula

y - b = m(x - a)

what does the discriminate, b² - 4ac, tell you

> 0: multiple x-int

= 0: 1 x-int

< 0: no x-int

when an > 0, which way does an even and odd have an effect on the direction the graph

n = even: up

n = odd: down

when an < 0, which way does an even and odd have an effect on the direction the graph

n = even: down

n = odd: up

What’s the format for power functions

f(x) = x^a (a: constant)

What’s the format for exponential functions

f(x) = b^x (b: a positive constant)

What’s the addition and subtraction rule for positive bases

b^m+n = b^m * b^n

b^m-n = b^m/b^n

What do the graphs look like for y = b^x (bases)

0 < b < 1: Downward exponential slope

b > 1: Exponential Slope

What’s the side ratios for a pi/4, pi/4, 90 triangle

root(2),1, 1

What’s the side ratios for a pi/3, pi/6, 90 triangle

root(3), 1, 2

What values are zero and the peak (1) in a sin graph

pi, 2pi =>zero

pi/2, 3pi/2 => 1

What values are zero and the peak (1) in a cos graph

pi/2, 3pi/2 =>  zero

pi, 2pi => 1

Name some trig properties

sin(theta + pi) = -sin(theta)

sin(theta + pi) = -cos(theta)

sin(-theta) = -sin(theta)

sin(-cos) = cos(theta)

sin²(theta) + cos²(theta) = 1