Increasing/Decreasing Intervals
Do we read the graph from left to right or right to left?
What is left to right.
True or False: Numbers are used in End Behavior.
What is false only x,y, and infinity are used.
What does fog stand for in function operations?
What is f(g(x)) f of g of x
F(x)=2x+6 x=2
What is f(2)=10
Given f(x)=x+6 and g(x)=x-2. How would you set up (f+g)(x)?
What is (f+g)(x)= 2x+7
True or False: Both x and y values are used when solving for Increasing/Decreasing Intervals.
What is false, only x values are used.
How is end behavior written?
What is x -> -∞,∞ & y-> -∞,∞
Given f(x)=x+4 and g(x)=x-7. How would you set up f(g(x))?
What is f(g(x))= (x-7)+4
f(x)=4x2+3 x=5
What is f(5)=103
Given f(x)=x-13 and g(x)=2x+1. How would you set up (f-g)(x)?
What is (f-g)(x)=-x-12
Describe what the increasing and decreasing intervals should look like on the graph?
What is the increasing interval is where the graph goes upward and the decreasing interval is where the graph goes downward.
What would the end behavior be for a graph ending in the bottom left-hand quadrant?
What is x-> -∞, y-> -∞
as x is approaching -∞, y is approaching -∞
Given f(x)=x2+4 and g(x)=x2-9. How would you set up g(f(x))?
What is g(f(x))= (x2+4)2-9
F(x)=x2+3x+11 x=0
What is f(0)=11
Given f(x)=3x2-9 and g(x)=3x+2. How would you set up (f+g)(x)?
What is (f+g)(x)=3x2+3x-7
Describe what the graph would look like for these intervals... increasing (-∞, -5) (6,∞) decreasing (-5, 6)
What is a graph increasing from -∞ (bottom left-hand) and stopping at the x-value -5. Then decreasing to the x-vaule 6 and then increasing to ∞(top right-hand).
What would the end behavior be for a graph ending in the top left-hand quadrant?
What is x->-∞, y-> ∞
as x is approaching -∞, y is approaching ∞
Given f(x)=5x2+3 and g(x)=-7x2+9. How would you set up f(g(x))?
What is f(g(x))= 5(-7x2+9)2+3
F(x)=8x2+2x-7 x=9
What is F(x)=659
Given f(x)=2x2 and g(x)=x. How would you set up (f/g)(x)?
What is (f/g)(x)=2x
Describe what the graph would look like for these intervals... decreasing (-∞,3) (7,-∞) increasing (3,7)
What is a graph decreasing from -∞ (top left-hand) and stopping at the x-value 3. Then increasing to the x-vaule 7 and then decreasing to -∞(bottom right-hand).
What would the end behavior be for a graph ending in the bottom right-hand quadrant?
What is x-> ∞, y-> -∞
as x is approaching ∞, y is approaching -∞
Given f(x)=2x2+6x+3 and g(x)=-3x2+5x. How would you set up f(g(x))?
What is f(g(x))= 2(-3x2+5x)2+6(-3x2+5x)+3
F(x)=x2-3x+5 x=6
What is F(6)=23
Given f(x)=x2+4 and g(x)=6x+6. How would you set up (fg)(x)?
What is (fg)(x)=6x3+6x2+24x+24