Composite Functions: Graphs, Tables and Charts

Composite Functions Lesson

​Graphs, Tables and Charts

At the end of the lesson, students will be able to:

• Define composite functions.

• Solve composite functions.

• Apply composite functions in real life.

​

​But first let's review.

Multiple Choice

Evaluate:  f(x) = 2x² + 5x - 17, find f(-1). 

• f(-1) = -20
• f(-1) = -24

Multiple Choice

Perform the indicated operation:

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f + g)(x).

• 11x² - 1
• 5x⁴ + 6x² - 1
• 5x² + 6x - 1
• 5x² + 8x - 1

Multiple Choice

Perform the indicated operation:

f(x) = 3x² + 7x and g(x) = 2x² - x - 1, find (f - g)(x).

• x² + 8x + 1
• x² + 6x - 1
• 5x² + 8x - 1
• x² + 8x -1

Multiple Choice

Perform the indicated operation: f(x)= x+3 g(x)= x-2 $$\left(\frac{g}{f}\right)\left(x\right)$$  

• $$\frac{x+3}{x-2}$$  

• $$\frac{x-2}{x+3}$$  

• -2/3

• 3/2

• It is an operation on functions

• You are multiplying f(x) and g(x) not substituting functions

Function Composition (Equations)

Function Composition Review

​Evaluate Composite Functions

Multiple Choice

Which one is the same as $$\left(f\circ g\right)(x)$$  

• g(f(x))

• f(g(x))

Multiple Choice

Which one is the same as $$\left(g\circ f\right)(x)$$  

• g(f(x))

• f(g(x))

Multiple Select

Given f(x) = 2x and g(x) = x²+3 , To compose f(g(x)) I would

Click all that apply.

• Substitute function g into function f

• Replace x with

  x² + 3

• Substitute function f into function g

• Replace x with

  2x

Multiple Choice

Given f(x) = 2x and g(x) = x²+3 , compose f(g(x)).

• x²+2x+3
• 4x²+3
• 2x²+3
• 2x²+6

Multiple Choice

p(x) = 3x + 4

q(x) = 2x²

Find p(q(x))

• 10x²

• 18x² + 4

• 6x² + 4

Watch the following video if you missed any of the previous problems.

(Equations)

Reorder

f(x) = 3x + 10

g(x) = x - 2

Order the steps to correctly evaluate f(g(3))

• Replace x with 3 in function g.

• Use order of operations to find g(3).

• Replace x with 1 in function f.

• Use the order of operations to find f(1).

1

2

3

4

• 1
• 2
• 3
• 4

Multiple Choice

If $$f\left(x\right)=2x$$   and  $$g\left(x\right)=2x^2-1$$   find $$g\left(f\left(-1\right)\right)$$  

• 2

• 15

• 7

• -9

​Evaluating Composite Functions Using Graphs

Multiple Select

Given f (red) and g (blue) in the graph,

Which statements are correct when evaluating $$(f\circ g)(-1)$$ ?

• First find the y value of function f at -1:

  f(-1) = 6

• Then find the y value of function g at x = 6:

  g(6) = 10

• First find the y value of function g at x = -1:

  g(-1) = 1

• Then find the y value of function f at 1:

  f(1) = 4

Multiple Choice

Given f (red) and g (blue) in the graph,

what is $$(f\circ g)(-1)$$   ?

• 1

• 4

• -1

• 6

Multiple Choice

Given f and g in the graph,

what is f(g(2)) ?

• 3

• 8

• 1

• 4

​What if the functions are on separate coordinate planes?

example 1​

example 2

Fill in the Blank

f(h(-4)) =

Fill in the Blank

f(g(5)) =

​Evaluating Composite Functions Using Tables

Multiple Choice

When evaluating h(f(-2)) I would first find ____ which is _____

• f(-2); -1

• h(-2); -2

• g(-2); -2

Multiple Choice

When evaluating h(f(-2)) next I would find ____ which is _____

• f(-1); 4

• h(-2); -2

• h(-1); 0

• f(2); 1

Fill in the Blank

h(f(-2)) =

Fill in the Blank

f(f(0)) =

Function Composition (Tables and Graphs)

Multiple Choice

• 6

• 8

• 15

• None of the Above

Multiple Choice

• 3

• 1

• 4

• None of the Above

Watch the following video if you missed the previous 2 problems

(Tables)

Multiple Choice

Evaluate $$(g\circ f)(0)$$  

• -5

• -3

• 0

• 1

Multiple Choice

Evaluate: $$(f\circ g)(1)$$  

• -5

• -3

• 0

• 1

Watch the following video if you missed the previous 2 problems.

(Graphs)