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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

3. Function Notation

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Exercise 33 Page 126

Practice makes perfect

a We are asked to write the given equation in function notation, and evaluate it for a given input value. Let's see an example of function notation.

f(x)=xIn the above equation, x and f(x) represent the input and output respectively. We will use this to rewrite the formula d=2r. This equation expresses the diameter d of a circle in terms of its radius r, where r is the input and d is the output. Let's write this formula using function notation. d(r)=2r To evaluate this function for r=5, we will substitute 5 for r in the above equation.

d(r)=2r

r= 5

d( 5)=2( 5)

Multiply

d(5)=10

The statement d(5)=10 means that a circle with a radius of 5 feet has a diameter of 10 feet.

b The given equation for the area of a circle is A=π r^2, where r is the input and A is the output. Let's write it using function notation.

A(r)=π r^2 To evaluate this function for r=5, we will substitute 5 for r in the above equation.

A(r)=π r^2

r= 5

A( 5)=π ( 5)^2

Calculate power

A(5)=π(25)

Multiply

A(5)=25π

▼

Simplify right-hand side

Use a calculator

A(5)= 78.539816...

Round to 1 decimal place(s)

A(5) ≈ 78.5

The statement A(5)=25 π means that a circle with a radius of 5 feet has an area of 25 π or about 78.5 square feet.

c The given equation for the circumference of a circle is C=2π r, where r is the input and C is the output. Let's write it using function notation.

C(r)=2π r To evaluate this function for r=5, we will substitute 5 for r in the above formula.

C(r)=2π r

r= 5

C( 5)=2π ( 5)

Multiply

C(5)= 10π

Use a calculator

C(5)= 31.415926...

Round to 1 decimal place(s)

C(5) ≈ 31.4

The statement C(5)=10 π means that a circle with a radius of 5 feet has a circumference of 10 π or about 31.4 feet.

Subchapter links

Communicate Your Answer p.121

Monitoring Progress p.122-124

Exercises p.125-126