Piecewise Functions
f(x) = -x+2 when x is less than or equal to 0
= 3x when x is greater than 0
What is f(6)?
f(6) = 18
What are the four functions we practiced transformations on and what do they look like?
absolute value, quadratics, square root, cubic
f(x) = 3x+5
g(x) = 6-2x
What is (f+g)(2)?
13
What are the three types of symmetry?
x-axis, y-axis, origin
When is a function even and when is it odd?
even when it is symmetric with respect to the y-axis, odd when it is symmetric with respect to the origin
f(x) = -x+2 when x is less than or equal to 0
= 3x when x is greater than 0
What is f(-2)?
f(-2) = 4
What order do I preform these transformations in?
a. reflection over x axis
b. stretch by 6
c. left 5
d. down 1
CDAB or CDBA
f(x) = 3x+5
g(x) = 6-2x
What is (f-g)(5)?
24
y=x2+9
y-axis
How can I algebraically determine when a function is even? When it is odd?
EVEN: f(-x) = f(x)
ODD: f(-x) = -f(x)
f(x) = -x+2 when x is less than or equal to 0
= 3x when x is greater than 0
What is our turning point and how many times do you plug it in?
turning point = 0
you plug it in to every equation, so 2 times
What transformations are occurring:
f(x) = -(x-7)2+9
reflection over the x-axis, right 7, up 9
f(x) = 3x+5
g(x) = 6-2x
What is (f/g)(x)?
3x+5 / 6-2x
y=x3-4x
origin
f(x) = x4-9x2
even
f(x) = -x+2 when x is less than or equal to 0
= 3x when x is greater than 0
What is f(-1)?
f(-1) = 3
What transformations are occurring:
f(x) = 9(x-2)3+2
VS BAFO 9, right 2, up 2
f(x) = 3x+5
g(x) = 6-2x
What is (fg)(x)?
8x-6x2+30
x+y2=7
x-axis
f(x) = x3-3x2-5x
Neither
f(x) = -x+2 when x is less than or equal to 0
= 3x when x is greater than 0
What is f(0)?
f(0) = 2
Using the cubic function , write the equation that reflects across the x-axis, compresses by 5/7, and moves left 6
f(x) = -5/7(x+6)
f(x) = 3x+5
g(x) = 6-2x
What is (g of f)(x)?
-4-6x
x2+y2=18
x-axis, y-axis, origin
f(x) = x3 +9x
odd