Bell Assignment:

In a particular county, the population fo the two largest cities can be modeled by f(x)=200x+25 and g(x)=175x-15, where x is the number of years since 2000 and the population is in thousands.

1

What is the population of the two cities combined after any number of years?

1

How much larger is the largest city?

Notes L6-1b: Composition of Functions

1

What does
mean?

plug 5 into f

mutilipy f times 5

1

What does
mean?

mutilipy f and g and 5

plug 5 into g and that answer into f

plug 5 into f and that answer into g

Given:

f(x)=5x

g(x)=-2x+1

h(x)=x^{2}+6x+8

Evaluate [5], [6], [7]:

1

f[g(-2)]

1

g[g(3)]

1

h[f(-5)]

1

What does
mean?

plug g into f

mutilipy f and g

plug f into g

multiply f, g and x

1

f(x)=2x
g(x)=x+5
Evaluate [f ∘ g]

1

f(x)=2x
g(x)=x+5
Evaluate [g ∘ f]

1

f(x)=x-4
g(x)=x^{2}-10
Evaluate [f ∘ g]

1

f(x)=x-4
g(x)=x^{2}-10
Evaluate [g ∘ f]

f(x)=x+5

g(x)=3x-7

1

Evalutate [f ∘ g]

1

Evaluate [g ∘ f]

1

Evaluate (f \cdot g)

1

What does the following mean? How would you evaluate it?

1

Given f(x)=5x
g(x)=-2x+1
h(x)=x^{2}+6x+8
Evaluate: \left[f\ ∘\ h\ ∘\ g\right]\left(-3\right)

1

To evaluate g (f (-3)), which should you find first?

1

Evaluate g (f (-3)) from [18].

0

Choose all that are true

I am confident in this lesson.

I would like some assistance.

I can compose two functions for a numerical evaluation.

I can compose two functions: \left[f\ ∘\ g\right]\left(x\right)

103 Compostions of Functions

Notes L6-1b: Composition of Functions

103 Compostions of Functions

Bell Assignment:

What is the population of the two cities combined after any number of years?

How much larger is the largest city?

Notes L6-1b: Composition of Functions

What doesmean?

What doesmean?

f[g(-2)]

g[g(3)]

h[f(-5)]

What doesmean?

f(x)=2xg(x)=x+5Evaluate [f ∘ g]

f(x)=2xg(x)=x+5Evaluate [g ∘ f]

f(x)=x-4g(x)=x^{2}-10Evaluate [f ∘ g]

f(x)=x-4g(x)=x^{2}-10Evaluate [g ∘ f]

Evalutate [f ∘ g]

Evaluate [g ∘ f]

Evaluate (f \cdot g)

What does the following mean? How would you evaluate it?

Given f(x)=5xg(x)=-2x+1h(x)=x^{2}+6x+8Evaluate: \left[f\ ∘\ h\ ∘\ g\right]\left(-3\right)

To evaluate g (f (-3)), which should you find first?

To evaluate g (f (-3)), which should you find first?

Evaluate g (f (-3)) from [18].

Choose all that are true

Bell Assignment:

What is the population of the two cities combined after any number of years?

How much larger is the largest city?

What doesmean?

What doesmean?

f[g(-2)]

g[g(3)]

h[f(-5)]

What doesmean?

f(x)=2xg(x)=x+5Evaluate [f ∘ g]

f(x)=2xg(x)=x+5Evaluate [g ∘ f]

f(x)=x-4g(x)=x^{2}-10Evaluate [f ∘ g]

f(x)=x-4g(x)=x^{2}-10Evaluate [g ∘ f]

Evalutate [f ∘ g]

Evaluate [g ∘ f]

Evaluate (f \cdot g)

What does the following mean? How would you evaluate it?

Given f(x)=5xg(x)=-2x+1h(x)=x^{2}+6x+8Evaluate: \left[f\ ∘\ h\ ∘\ g\right]\left(-3\right)

To evaluate g (f (-3)), which should you find first?

To evaluate g (f (-3)), which should you find first?

Evaluate g (f (-3)) from [18].

Choose all that are true

What does
mean?

What does
mean?

What does
mean?

f(x)=2x
g(x)=x+5
Evaluate [f ∘ g]

f(x)=2x
g(x)=x+5
Evaluate [g ∘ f]

f(x)=x-4
g(x)=x^{2}-10
Evaluate [f ∘ g]

f(x)=x-4
g(x)=x^{2}-10
Evaluate [g ∘ f]

Given f(x)=5x
g(x)=-2x+1
h(x)=x^{2}+6x+8
Evaluate: \left[f\ ∘\ h\ ∘\ g\right]\left(-3\right)

What does
mean?

What does
mean?

What does
mean?

f(x)=2x
g(x)=x+5
Evaluate [f ∘ g]

f(x)=2x
g(x)=x+5
Evaluate [g ∘ f]

f(x)=x-4
g(x)=x^{2}-10
Evaluate [f ∘ g]

f(x)=x-4
g(x)=x^{2}-10
Evaluate [g ∘ f]

Given f(x)=5x
g(x)=-2x+1
h(x)=x^{2}+6x+8
Evaluate: \left[f\ ∘\ h\ ∘\ g\right]\left(-3\right)