Graphing Overview, Linear systems, and Functions

Graphing overview

100

Find the intercepts of the following equation and graph:

2x+y=4

x=(2,0)

y=(0,4)

200

Graph the following and then find where the equations intersect:

y=3

x=-2

(-2,3)

300

Graph the following equation and find where they intersect:

y=-3x+4

y=3x-2

(1,1)

400

Graph the following and find where they intersect:

4x+2y=10

x-y=13

(6,-7)

500

Graph the following equations and find where they intersect:

y=-2/3x-2

y=-8/3x+4

(3,-4)

Solving system of equations by substitution and elimination

100

Solve by substitution:

3x+2y=3

−2x− y=-1

x=-1

y=3

200

Solve by elimination:

3x+2y=−1

4x− 5y=14

x=1

y=-2

300

Solve the following using elimination:

x/3 - y/2 = 1

x/4 + y = 2

(0,-2)

400

Solve by substitution:

2x - y = -4

6x - 3y = -12

infinite number of solutions

500

Solve the following using substitution:

3x−2y=7

y=3/2x + 5

no solution

Solving system of equations word problems

100

Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.

small box of oranges: $7, large box of oranges: $13

200

You and a friend go to Tacos Galore for lunch. You order three soft tacos and three burritos and your total bill is $11.25. Your friend's bill is $10.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost?

(1.25,2.5)

x = the price of 1 soft taco

y= the price of 1 burrito

300

You are running a concession stand at a basketball game. You are selling hot dogs and sodas. Each hot dog costs $1.50 and each soda costs $0.50. At the end of the night you made a total of $78.50. You sold a total of 87 hot dogs and sodas combined. You must report the number of hot dogs sold and the number of sodas sold. How many hot dogs were sold and how many sodas were sold?

(35,52)

35 hot dogs and 52 sodas were sold

400

Each polio vaccination consists of 4 doses, and each measles vaccination consists of 2 doses. Last year, Doctor gave a total of 60 vaccinations that consisted of a total of 184 doses. How many polio vaccinations and how many measles vaccinations did Doctor give last year?

Doctor gave 32 polio vaccinations and 28 measles vaccinations.

500

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

1500 children and 700 adults

Find the Domain

100

Find the domain and write it in interval notation:

f(x)=x^3-4

(-inf,inf)

200

Find the domain of the following function and write in interval notation:

f(x)=1/x+5

(-inf,-5) U (-5,inf)

300

Find the domain and write it in set notation:

y= *square root*(2x+8)

{x|x greater than or equal to -4}

400

Find the domain and write it in interval notation:

y=*square root*(x^2-25) / 3x-24

(-inf,-5] U [5,8) U (8,inf)

500

Find the domain and write in set notation:

y=*square root*(9-x^2) / (x^2+7x+10)

{x|-3 less than or equal to x less than or equal to 3, x cannot equal -2}