Unit 1
What is the equation for a linear relationship?
y=m(x)+b
What is function notation?
Function Notation - A standardized way to name and write functions ex. f(x)
What is linear growth or decay?
Something that gets bigger or smaller but goes up or down by a constant number
Solve the equation to find (x,y)
8x+2y=16
(-4,8)
Function P gives the weight of a puppy, in kilograms, when it is m months old. What does this mean in terms of the situation? P(4)=7
4 is the weight after 7 months
7 is the number of months
What is a system of equations?
a set of 2+ equations with the same variables and is solved together to find values
Ex. x + y = 5
x - y = 1
What is Rate of Change?
Rate of change - Measures how one variable changes in relation to another
What is exponential growth or decay?
An amount that goes up or down but is doubled or multiplied/divided by a different number each time
Solve the system of equations
x+2y=8
x=-5
x=-5
y=6.5
Function P gives the weight of a puppy, in kilograms, when it is m months old. What does this mean in terms of the situation? P(2.5)
Puppy's weight (x), after 2.5 months
What is the standard form equation for a line?
a(x)+b(y)=c
What is the domain and range?
Domain - all possible "x" values
Range - all possible "y" values
What happens to the exponents?
x^2+x^3
You add
x^5
Solve the equation 17.5x+12.5y=700 and find x
SUBSTITUTE 0 FOR Y
x=40
Function P gives the weight of a puppy, in kilograms, when it is m months old. What does this mean in terms of the situation? P(m)=18
Puppys weight (18) after m months
When solving inequalities, if you multiply or divide by a negative number, what happens to the inequality sign?
You flip the inequality because you divided or multiplied by a negative
f(x)=f(b)-f(a) over b-a
What happens to the exponents?
(x^4)^2
You multiply
x^8
Solve the system of equations
5x-2y=26
y+4=x
x=6
y=2
Function P gives the weight of a puppy, in kilograms, when it is m months old. What does this mean in terms of the situation? P(4)>P(2)
The puppys weight is greater after 4 months than 2 months
What is substitution and elimination when solving equations?
Substitution - replacing a variable with a number or expression. ex. replacing x for y+4 because y+4=x
Elimination - adding or subtracting the equations to eliminate a variable to simplify the problem. ex. 4x - 4x means the "x" would cancel out
What is an inverse function?
Inverse Function - Two functions are inverses to each other if their input-output pairs are reversed.
What happens to the exponents?
x^-4
Flip base to other side of the fraction and make exponent positive
1/4x
Solve the system of equations
4x+3y=10
-4x+5y=6
x=1
y=2
Function P gives the weight of a puppy, in kilograms, when it is m months old. What does this mean in terms of the situation? P(2)<P(3)
The weight of a puppy after 2 months is less than after 3 months