# Graph and Function

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.