Functions
& Graphs
& Graphs
The difference quotient of f(x) = x2 - 4x + 2.
What is 2x + h - 4 ?
Exact solution(s) for x2-6x+34=0, as solved with the quadratic formula.
What are {3+5i} and {3-5i} ?
The logarithmic form of 94 = x.
What is 4 = log9x ?
The solution, via substitution, of:
2x - 3y = 26 - 5x
9x + 3y = x + 2y + 43
What is (5,3) ?
The equation for the line passing through (-3,11) and (2,-4).
What is y = -3x + 2?
One of the rational zeroes of f(x) = 7x3 - 5x2 - 63x + 45.
What is 5/7, 3, or -3 ?
The full expansion (and non-calculator evaluation) of
ln root4 x.
What is
1/4 lnx ?
You invest in a new play. The cost includes an overhead of $42,500, plus production costs of $2500 per performance. A sold-out performance brings in $3125. This is the cost function C(x), where x represent the number of sold-out performances.
What is C(x) = 42,500 + 2500x ?
The two functions f and g so that h(x)=(f◦g)(x), where one of the functions is 5x-3 and h(x)=(5x-3)6.
What are f(x)=x6 and g(x)=5x-3 ?
The solution of 5x2 + 8x < -3.
What is ( -1, -3/5 ) ?
The full expansion (and non-calculator evaluation) of
log_b((x^3y)/(z^5)) .
What is 3logbx + logby - 5logbz ?
You invest in a new play. The cost includes an overhead of $42,500, plus production costs of $2500 per performance. A sold-out performance brings in $3125. This is the revenue function R(x), where x represent the number of sold-out performances.
What is R(x) = 3125x ?
This is the yield per tree, Y, in pounds, as a function of the number of lemon trees per acre, x, where x is greater than 125; Given that the annual yield per lemon tree is fairly constant at 330 pounds per tree when the number of trees per acre is 125 or fewer. For each additional tree over 125, the annual yield per tree for all trees on the acre decreases by 4 pounds due to overcrowding.
What is Y(x) = -4x + 830 ?
The solution set of
(7x+1)/(5x-3) ≤ 2
What is ( -∞, 3/5 ) ⋃ [ 7/3, ∞ ) ?
The solution set of 2log(x) = log(100).
What is { 10 } ?
The solution(s) of the system:
x2 + (y-6)2 = 25
x2 - 5y = -5
What is { (0,1), (-5,6), (5,6) } ?
The area of the field, A, as a function of one of its dimensions, x; Given that you have 1000 feet of fencing to enclose a rectangular field.
What is A(x) = 500x - x2 ?
Radiation machines, used to treat tumors, produce an intensity of radiation that varies inversely as the square of the distance from the machine. At 3 meters, the radiation intensity is 62.5 milliroentgens per hour.
This is the intensity at a distance of 1.8 meters, rounded to the nearest tenth as needed.
What is 173.6 milliroentgens per hour?
The re-written version of y = 105(6.9)x in terms of base e. (Rounding any natural logarithms to three decimal places.)
What is y=105e1.932x ?
Food and clothing are shipped to victims of a natural disaster. Each carton of food will feed 9 people, while each carton of clothing will help 4 people. Each 20ft3 box of food weighs 50 pounds and each 5ft3 box of clothing weighs 25 pounds. The commercial carriers transporting food and clothing are bound by the following constraints (a) The total weight per carrier cannot exceed 24,000 pounds. (b) The total volume must be no more than 7000ft3.
This is the number of cartons of food and clothing that will maximize the number of people who can be helped.
What are 220 cartons of food and 520 cartons of clothing?