Graph and Function

Concept/ writing Exercise. Please show your work as detailed as possible.

1 what is a relation? Explain

2. Are all relations also function? Explain.

3. What is the domain of a function?

4. What are the domain and range of the function f(X) = 2x +1? Explain your answer.

5. What are the domain and range of a function of the form f(X) = ax+b, a ≠ 0? Explain your answer.

6. What is a dependent variable?

7. How is “f(x)” read?

In exercise 8-10 a) determine if the relation illustrated is a function b) Give the domain and range of each function or

relation. Please show your work as detailed as possible.

8. Nicknames

Robert Bobby

Rob

Margaret Peggy

Maggie

9. a number

4 16

5 25

7 49

10. absolute value

[-8] 8

[8]

[0] 0

In exercise 11-14 a) determine which of the following are function. b) Give the domain and range of each relation or

function.

11. {(1,0), (4, 2), ( 9,3), ( 1, -1), (4, -2), (9, -3)}

12. {(-1,1),(0,-3), (3,4), (4,5), (-2,-2)}

13. {(6,3),(-3,4), (0,3), (5,2),(3,5), (2,8)}

14. { (3,5), (2,5), (0,5),(-1,5)}

Evaluate each function at the indicated values. Please show your work as detailed as possible.

f(X) =-2X+7; find a) f(2) b) f(-3)

f(a)= 1/3a + 4; find a) f(0) b) f(-12)

h(x)=x^2 –x-6; find a) h(0) b) h(1)

g(x) =-2X^2+7X-11; find a) g(2). b) g(1/2)

r(t) =〖-t〗^(3 )-2t^2+t+4; find a) r(1) b) (-2)

g(t)= 4-3t+16t^2 -2t^3; find a) g(0) b) (3)

h(z)=|5-2z|; find a) h(6) b) (5/2)

q(x)= -2|x+8|+13; find a)q(0) b) (-4)

s(t)= √(t+3); find a) s(-3) b) s(6)

f(t)= √(5-2t); find a) f(-2) b) f(2)

g(x)= (x^(3 )-2)/(x-2); find a) g(0) b) g(2)

h(x)=(x^2+4x)/(x+6); find a)h(-3) b)h(2/5).

Problem Solving.Please show your work as detailed as possible.

Area of rectangle. The formula for the area of a rectangle is A= lw. If the length of a rectangle is 6 feet, then

the area is a function of its width, A(w)=6w. Find the area when the width is a) 4 feet b) 6.5 feet.

Simple interest. The formula for the simple interest earned for a period of 1 year is i=pr, where p is the

principle invested and r is the simple interest rate. If $1000 is invested, the simple interest rate, i(r)= 1000r.

Determine the simple interest earned in 1 year if the interest rate is a) 2.5% b) 4.25.

Area of a circle. The formula for the area of a circle is A=πr^2. The area is a function of the radius. a) write

this function using function notation.b) determine the area when the radius is 12 yards.

Perimeter of square. The formula for the perimeter of a square is p=4s where s represents the length of any one of

the sides of the square.

write this function using function notation

Determine the perimeter of a square with sides of length 7 meters.

5. Temperature. The formula for changing Fahrenheit temperature into Celsius temperature is C=5/9 ( f-32). The Celsius

temperature is a function of Fahrenheit temperature.

Write this function using function notation.

Find the Celsius temperature that corresponds to-31°F.

6. Volume of cylinder. The formula for the volume of a right circular cylinder is V==πr^2 h. If the length, h, is 3 feet,

then the volume is a function of the radius, r.

a) Write this formula in function notation, where the height is 3 feet.

b) Find the volume if the radius is 2 feet.

7. Sauna Temperature.The temperature, T in degree Celsius, in a sauna n minute after being turned on is given by the

function T(n)= -0.03n^2+ 1.5n +14. Find the sauna’s temperature after.

a) 3minutes. b) 12minutes

8. Stopping Distance. The stopping distance, d in meters for a car traveling v kilometers per hours is given by the

function d(v)=0.18v + 0.01v^2. Find a) 60km/hr b) 25km/hr

9. Air conditioning. When an air conditioner is turned on maximum in a bedroom at 80°, the temperature, T, in the room

after A minute can be approximated by the function

T(A)=-0.02A^2- 0.34A +80, 0≤A≤15.

Estimate the room temperature 4 minutes after the air conditioner is turned on.

Estimate the room temperature 12 minutes after the air conditioner is turned on.

10. Accidents. The number of accidents, n, in 1 month involving drivers X years of age can be approximated by the function

n(X)= 〖2x〗^(2 )-150x + 4000. Find the approximate number of accident in 1 month that involved

a) 18 years olds

b) 25 years olds.

11. Oranges The total number of oranges, T, in a square pyramid whose base is n by oranges is given by the function. T(n)

=1/3n^3+1/2n^2+1/6n.

Find the number of oranges if the base is

6 by 6 oranges.

8 by 8 oranges.

12 Rock Concert. If the cost of a ticket to a rock concert is increased by X dollars, the estimated increased in revenue,

R in thousands of dollars is given by the function

R(X) = 24 + 5X-x^2, x<8. Find the increase in revenue if the cost of the ticket is increased by

$1.

$4.