Adding
f(x) = 3x - 4
g(x) = 7x - 3
What is f + g?
10x - 7
f(x) = 2x + 3
g(x) = 4x - 5
Will f - g(x) produce the same answer as g - f(x)?
No! Order matters when subtracting
f - g(x) = -2x + 8
g - f(x) = 2x - 8
f(x) = 2x + 4
g(x) = 3x
What is f • g?
6x2 + 12x
David owns a garden plot in his backyard. He wants to put fencing around the outside of the plot. The length and width of the garden is modeled by the functions L(x) and W(x) respectively. What expression, P(x), models the perimeter of the garden?
L(x) = 3x + 2
W(x) = x + 5
P(x) = 8x + 4
f(x) = 2x2 + 3x + 6
g(x) = x2 - 6x + 2
What is f + g(x)?
3x2 - 3x + 8
g(x) = 2x2 + 3x - 4
h(x) = 3x2 - 4x + 7
What is g - h(x)?
-x2 + 7x - 11
f(x) = x3 - 2x2 + 5x - 6
g(x) = x + 3
What is f • g?
x4 + x3 - x2 + 9x - 18
The area of Sue's yard can be modeled by the function Y(x) = 2x2 - 3x + 5. Sue wants to install an in-ground pool to use in the summertime. The area of the pool can be modeled by the function P(x) = x2 + 5x - 2. Write a function that represents the area of Sue's yard that will be remaining after the pool is installed.
x2 - 8x + 7
f(x) = 4x2 - 5x + 2
g(x) = 2x2 + x - 2
What is f(x) + g(x)?
6x2 - 4x
f(x) = 2x3 + x - 3
g(x) = 7x3 - 4x2 + 4
What is g - f(x)?
5x3 - 4x2 - x + 7
f(x) = x + 3
g(x) = 2x
h(x) = x
What is h • g(x) • f(x)?
2x3 + 6x2
Find an expression to represent the volume, V(x), of a storage box in terms of the height, x. The length of the storage box can be modeled by the function L(x) = 3x - 5 and the width of the storage box can be modeled by the function W(x) = 4x + 12.
V(x) = 12x3 + 16x2 − 60x
k(x) = 6x3 + 8x2 - 5x + 1
h(x) = -4x3 + 3x2 - 2x + 2
What is k + h(x)?
2x3 + 11x2 - 7x + 3
f(x) = 4x + 5
g(x) = x2 - 6x + 1
h(x) = 4x2 + 5x - 2
What is h(x) - g-f(x)?
3x2 + 15x + 2
a(x) = 4x - 2
b(x) = 3x2 + x + 7
c(x) = x2 + 4
What is a • c(x) + b(x)?
4x3 + x2 + 17x − 1
For 2025, a bookstore made a profit modeled by the function P(x) = 37x + 900 where x represents the number of books sold. The business's cost for the year is modeled by the function C(x) = 12x + 300. How much revenue did the bookstore make if they sold 1200 books?
$60,000
a(x) = 3x2 - 4x + 2
b(x) = 2x - 5
c(x) = x3 + 2x2 + 9
What is a + b(x) + c(x)?
x3 + 5x2 - 2x + 6
a(x) = 5x3 + 2x - 4
b(x) = 2x3 + 8x2 - 3x + 2
c(x) = 3x2 - x + 6
What is b-c(x) + a-b(x)?
5x3 - 3x2 + 3x - 10
DOUBLE JEOPARDY CHALLENGE QUESTION:
f(x) = -3x2 + 4x - 6
g(x) = 2x3 + 5x - 1
h(x) = 5x + 2
What is f • g (x) + h • h(x)?
−6x5 + 8x4 − 27x3 + 48x2 − 14x + 10
A shipping company delivers packages to people in Tennessee. If the company's revenue per package, x, is modeled by R(x) = 45x and their cost to deliver the packages is modeled by C(x) = 5x + 1500 , how many packages must the company deliver to break even?
150 Packages