Adding/Subtracting Polynomials
(s^2+3s^3-3)+(2s^2+7s-2s^3)
s^3+3s^2+7s-3
3x^2(2x^4)
6x^6
How could you rewrite this:
(g \circ f)(x)
g(f(x))
What's the highest exponent in a polynomial called?
Degree
f(x) = water
g(x) = teabag
What would f(g(x)) mean?
Putting a teabag in water
(-1+x^2+2x)+(1-2x+2x^2)
3x^2
3s(2s+4s^2-5)
12s^3+6s^2-15s
Find:
(f \circ g)(x)
f(x)=6x+1
g(x)=4x
(f \circ g)(x)=24x+1
What is the number that stands alone in an expression called?
Constant
f(x) = Water
g(x) = Ice
What would f(g(x)) mean?
Iced Water
(-7k^5+14-2k)+(10k^4+7k+5k^5)
-2k^5+10k^4+5k+14
(x-2)(x+6)
x^2+4x-12
Find
(g \circ f)(1)
f(x)=x-1
g(x)=x^2+2x-8
(g \circ f)(1)=-8
What is the number in front of the highest degree term called?
Leading Coefficient
DOUBLE POINTS:
f(x) = chocolate
g(x) = milk
What would g(f(x)) mean?
Chocolate Milk
(k^2+6k^3-4)-(5k^3+7k-3k^2)
k^3+4k^2-7k-4
(3x-6)(5x+3)
15x^2-21x-18
Find:
(f \circ g)(x)
f(x)=x^2+7
g(x)=x-3
(f \circ g)(x)=x^2-6x+16
Describe the end behavior of
f(x)=2x^4+6
x to \infty , f(x) to \infty
x to -\infty, f(x) to \infty
f(x) = cookie
g(x) = milk
What would g(f(x)) mean?
Dip cookie in milk
(2a-3a)-(a^2-2a+4)
-a^2+a-4
(a-1)(−8a^2−6a−12)
-8a^3+2a^2-6a+12
You find a shirt at the store that is $10 off. Sales taxes in Anaheim is about 8%. The shirt's original price was $20. How much will the shirt cost after taxes?
You spent $10.80
DOUBLE POINTS:
What is a sum of terms, each of which is a constant times a whole number power of x called?
Polynomial
f(x) = shirt
g(x) = hoodie
What would f(g(x)) mean?
Shirt over Hoodie
(3-6x^5-8x^4)-(-6x^4-3x-8x^5)
2x^5-2x^4+3x+3
(3k+2)^3
27k^3+54k^2+36k+8
DOUBLE POINTS:
You receive a $20 gift card for shoes. The store is having a buy one, get one 10% off deal. You buy 2 shoes that each cost $40. How much did you spend at the store?
You spent $56
Describe the end behavior of
g(x)=-x^3+2x-4
x to \infty , g(x) to -\infty
x to -\infty, g(x) to \infty
f(x) = bagel
g(x) = cream cheese
What would g(f(x)) mean?