Shifting
What is the new function if f(x)=x2 is shifted up by 4 units
f(x)=x2+4
The domain of a function tells you all the possible values for THIS variable.
The X-value
You invest $120 at 6% for 1 year. What is the final amount?
$127.20
A=120(1+0.06*1)=120(1.06) =127.20
This method of solving systems involves graphing both equations and finding the point where the lines do THIS.
Intersect
What is the new function if f(x)=x2 is shifted left by 2 units
f(x)=(x+2)2
For the function f(x)=3x-5, the domain is all of these types of numbers.
All real numbers
You borrow $350 at 4% for 2 years. What is the final amount?
$378
A=350(1+0.04*2)=350(1.08)=378
In the system
y=2x+3
y=2x-4
the lines have THIS relationship, meaning there is no solution.
Parallel
What is the new function if f(x)=|x|+2 is shifted down by 3 units
f(x)=|x|-1
The range of a function represents all possible values of THIS variable.
The Y-values
You invest $80 at 7% for 3 years. How much interest do you earn?
$16.80
A=80(1+0.07⋅3)=80(1.21)=96.80
Interest = 96.80−80=16.80
THIS method eliminates one variable by adding or subtracting equations
The Elimination Method
What is the new function if f(x)=x3 is shifted right by 5 units
f(x)=(x-5)3
The function f(x) =-2x^2 + 8 is a parabola that opens downward. What is its range.
y≤ 8
You borrow $500 at 9% for 6 months. What is the final amount? (Hint: 6 months is half a year)
$522.50
A=500(1+0.09*0.5)=500(1.045)=522.50
Solve the system
3x+y=10
x-y=2
What is the value of X
3
What happens to the graph of f(x)=|x| when it becomes -f(x)
It is reflected across the x-axis (V-shape flips upside down!)
The function f(x)=4x-7 is linear. What is its domain.
All Real Numbers
You invest $240 at 3.5% for 4 years. How much interest is earned?
$33.60
A=240(1+0.035⋅4)=240(1.14)=273.60
Interest = 273.60−240=33.60
Solve the system
2x+3y=12
3x-y=2
What is the value of y
2