Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
SlideShare a Scribd company logo

119 Powerpoint 2.6

•Download as PPT, PDF•
•
J
Jeneva Clark

The document discusses different types of combinations and operations that can be performed on functions: 1. Arithmetic combinations include adding, subtracting, multiplying, and dividing two functions. 2. Composite functions involve composing one function with another, written as f(g(x)), where the output of g(x) becomes the input for f(x). 3. Decomposition of functions involves breaking a complex function down into simpler component functions, written as (fog)(x) where g(x) is the inner embedded function.

Related slideshows

Day 6 examples
Day 6 examplesDay 6 examples
Day 6 examples
 
5 4 function notation
5 4 function notation5 4 function notation
5 4 function notation
 
2.1 the basic language of functions t
2.1 the basic language of functions t2.1 the basic language of functions t
2.1 the basic language of functions t
 
1 of 15
2.6 Combinations of Functions: Composite Functions Arithmetic Combinations of Functions Composition of Functions Decomposition of Functions
A. If f(x) = 2x – 3 and g(x) = x 2 – 1 Find f(x) + g(x). Skeleton: ( ) + ( ) The nickname for f(x) + g(x) is _________.
If f(x) = 2x – 3 and g(x) = x 2 – 1 Find f(x) – g(x). Skeleton: ( ) – ( ) Nickname for f(x) – g(x) is ____________.
If f(x) = 2x – 3 and g(x) = x 2 – 1 Find f(x)g(x). Skeleton: ( )( ) The nickname for f(x)g(x) is ___________
If f(x) = 2x – 3 and g(x) = x 2 – 1 Find Skeleton: The nickname for this one is:
You try: f(x)=2x+1, g(x)=x 2 +2x-1 A) Find (f + g)(x) B) Find (f – g)(x) C) Find (f + g) (-1) D)Find (fg)(x).
B. Composition of Functions means f(g(x)), like “f of g of x” Plug g INTO f. Make skeleton of f first, and then plug in the whole g(x) expression
Write it as “f(g(x))” (means plug g into f) Write skeleton of f: (________) + 2 Into the blanks, put what g(x) is equal to. ( 4 – x 2 ) + 2 Simplify: Find if f(x) = x + 2 and g(x) = 4 – x 2
Find if f(x) = x + 2 and g(x) = 4 – x 2 If asked to find
You try: f(x) = x 2 , g(x) = x - 1
Finding these from a graph: If I say “Find f(2),” the 2 is an X-VALUE! On a graph, you would go to the 2 on the x-axis, and look up and down until you find the graph called “f(x)” and you would find it’s Y-VALUE at the point. (Recall that “f(x)” is another way of saying “the y-value on this certain function.”)
Here is an example, “Find f(2)”
Find these from the graphs:
C. Decomposition of Functions It is an important skill in calculus to be able to take a fancy function and to break it down into simpler parts. Watch this: h(x) = (1 – x) 3 Imagine that fancy part on the inside were just a plain x. One function would be and one would be . If it said, “Write this as (fog)(x),” the g(x) would be the inside one, the embedded one.
Try: Find two functions f and such that (fog)(x) = h(x).

More Related Content

119 Powerpoint 2.6

  • 1. 2.6 Combinations of Functions: Composite Functions Arithmetic Combinations of Functions Composition of Functions Decomposition of Functions
  • 2. A. If f(x) = 2x – 3 and g(x) = x 2 – 1 Find f(x) + g(x). Skeleton: ( ) + ( ) The nickname for f(x) + g(x) is _________.
  • 3. If f(x) = 2x – 3 and g(x) = x 2 – 1 Find f(x) – g(x). Skeleton: ( ) – ( ) Nickname for f(x) – g(x) is ____________.
  • 4. If f(x) = 2x – 3 and g(x) = x 2 – 1 Find f(x)g(x). Skeleton: ( )( ) The nickname for f(x)g(x) is ___________
  • 5. If f(x) = 2x – 3 and g(x) = x 2 – 1 Find Skeleton: The nickname for this one is:
  • 6. You try: f(x)=2x+1, g(x)=x 2 +2x-1 A) Find (f + g)(x) B) Find (f – g)(x) C) Find (f + g) (-1) D)Find (fg)(x).
  • 7. B. Composition of Functions means f(g(x)), like “f of g of x” Plug g INTO f. Make skeleton of f first, and then plug in the whole g(x) expression
  • 8. Write it as “f(g(x))” (means plug g into f) Write skeleton of f: (________) + 2 Into the blanks, put what g(x) is equal to. ( 4 – x 2 ) + 2 Simplify: Find if f(x) = x + 2 and g(x) = 4 – x 2
  • 9. Find if f(x) = x + 2 and g(x) = 4 – x 2 If asked to find
  • 10. You try: f(x) = x 2 , g(x) = x - 1
  • 11. Finding these from a graph: If I say “Find f(2),” the 2 is an X-VALUE! On a graph, you would go to the 2 on the x-axis, and look up and down until you find the graph called “f(x)” and you would find it’s Y-VALUE at the point. (Recall that “f(x)” is another way of saying “the y-value on this certain function.”)
  • 12. Here is an example, “Find f(2)”
  • 13. Find these from the graphs:
  • 14. C. Decomposition of Functions It is an important skill in calculus to be able to take a fancy function and to break it down into simpler parts. Watch this: h(x) = (1 – x) 3 Imagine that fancy part on the inside were just a plain x. One function would be and one would be . If it said, “Write this as (fog)(x),” the g(x) would be the inside one, the embedded one.
  • 15. Try: Find two functions f and such that (fog)(x) = h(x).