Tutors Answer Your Questions about Functions (FREE)
Question 1202118: For x∈[−11,12] the function f is defined by
f(x)=x4(x−4)7
On which two intervals is the function increasing?
to
and
to
Find the region in which the function is positive:
to
Where does the function achieve its minimum?
Click here to see answer by Alan3354(69443)   |
Question 1202213: (Comparing Functions) A pizza restaurant near a college uses the equation y = 3.25x + 4.25 to calculate the price of a pizza, y, with x number of toppings. A pizza restaurant in a mall uses the table below to calculate the price of the same size pizza.
Click here to see answer by mananth(16946)  |
Question 1202213: (Comparing Functions) A pizza restaurant near a college uses the equation y = 3.25x + 4.25 to calculate the price of a pizza, y, with x number of toppings. A pizza restaurant in a mall uses the table below to calculate the price of the same size pizza.
Click here to see answer by ikleyn(52794)  |
Question 1202248: A scientist is monitoring cell division and notes that a single cell divides into 4 cells within one hour. During the next hour, each of these cells divides into 4 cells. This process continues at the same rate every hour.
Part A. What type of function could be used to represent this situation?
Part B. Justify your reasoning.
Click here to see answer by math_tutor2020(3817) |
Question 1202464: The amount of money that a magazine pays for an article varies directly as the number of words in the article. If the magazine pays $720 for a 1200-word article, how much will be paid for an article of 1500 words?
Click here to see answer by ikleyn(52794) |
Question 1203019: I have a problem with questions relating to variation as the sum of two parts.
Here is a worked example.
A quantity, p, is the sum of two terms, one of which is constant while the other varies inversely as the square of q.
When q = 1, p=-1;
when q = 2, p=2;
find the positive value of q when p=2.75
If a and b are constants, p=a+b/q2;
q = 1, p= -1
-1 = a +b/12;
therefore -1 = a+b (equation 1)
when q = 2, p=2
2 = a+b/22
2=a+b/4
8 = 4a+b (equation 2)
Subtracting equation 1 from 2 gives
9=3a
so a =3
Substituting a = 3 into equation 1 we get
-1 = 3+b
b=-4
so p=3-4/q2
so when p = 2.75, 2.75 = 3-4/q2
4/q2 = ¼
q2 = 16
q=+/- 4 and we want the positive value so q = 4
I have tried to apply the same approach to the following problem:
A quantity C is the sum of two parts. The first part varies directly as the cube of t;
the second part varies inversely as the square of t.
C = 74, t = 1
C = 34, t = 2
Find C when t = 3
I wrote C = a3 +b/t2
74 = a3+b/12
74 = a3 +b (equation 1).
34 = a3+b/22
34 = a3+b/4
136 = 4a3+b (equation 2)
Subtract equation 1 from 2
136 = 4a3+b
74 = a3 +b
This gives 62 = 3a3
a3 = 20.67
a = 2.74
Substituting into the first equation
74 = 20.67 + b/12
74 = 20.67+b
b=53.33
To find C when t = 3
C = a3+b/t2
C = 20.67 + 53.33/9
9C = 186.03+53.33
9C = 239.36
C = 25.6 but the answer is 62.
Where have I gone wrong?
Click here to see answer by Theo(13342)  |
Question 1203019: I have a problem with questions relating to variation as the sum of two parts.
Here is a worked example.
A quantity, p, is the sum of two terms, one of which is constant while the other varies inversely as the square of q.
When q = 1, p=-1;
when q = 2, p=2;
find the positive value of q when p=2.75
If a and b are constants, p=a+b/q2;
q = 1, p= -1
-1 = a +b/12;
therefore -1 = a+b (equation 1)
when q = 2, p=2
2 = a+b/22
2=a+b/4
8 = 4a+b (equation 2)
Subtracting equation 1 from 2 gives
9=3a
so a =3
Substituting a = 3 into equation 1 we get
-1 = 3+b
b=-4
so p=3-4/q2
so when p = 2.75, 2.75 = 3-4/q2
4/q2 = ¼
q2 = 16
q=+/- 4 and we want the positive value so q = 4
I have tried to apply the same approach to the following problem:
A quantity C is the sum of two parts. The first part varies directly as the cube of t;
the second part varies inversely as the square of t.
C = 74, t = 1
C = 34, t = 2
Find C when t = 3
I wrote C = a3 +b/t2
74 = a3+b/12
74 = a3 +b (equation 1).
34 = a3+b/22
34 = a3+b/4
136 = 4a3+b (equation 2)
Subtract equation 1 from 2
136 = 4a3+b
74 = a3 +b
This gives 62 = 3a3
a3 = 20.67
a = 2.74
Substituting into the first equation
74 = 20.67 + b/12
74 = 20.67+b
b=53.33
To find C when t = 3
C = a3+b/t2
C = 20.67 + 53.33/9
9C = 186.03+53.33
9C = 239.36
C = 25.6 but the answer is 62.
Where have I gone wrong?
Click here to see answer by greenestamps(13200)  |
Question 1203113: An employee starts work on 1 January 2000 on an annual salary
of $30,000. His pay scale will give him an increase of $800 per
annum on the first of January until 1 January 2015 inclusive. He
remains on this salary until he retires on 31st December 2040.
How much will he earn during his working life.
Click here to see answer by ikleyn(52794) |
Question 1203646: The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g and choose the correct graph of g.
The graph of f(x) = |x| is shifted 3 units to the left and 4 units up.
g(x) =
Can you please explain me this homework question by showing the step-by-step calculations? Thank you so much!
Click here to see answer by MathLover1(20850)  |
Question 1203678: 2. A stone is dropped into a liquid forming circles which increase in radius with time according to the formula r(t) = 4t The area of a circle related to radius is A(r) = pi * r ^ 2 Using composition of functions, find an equation that would give area as a function time .
Click here to see answer by greenestamps(13200) |
Question 1203720: The graph of  is stretched horizontally by a factor of 2, reflected across the x-axis, and translated vertically upward by 3 units.
a) Determine the equation that results from these transformations.
b) Graph the Function. please include the image of key points under transformations.
Gyazo (or another tool) would work to capture the graph as an image and share as a link. Thank you!
Click here to see answer by MathLover1(20850) |
Question 1203721: In Canada we pay both federal and provincial income tax (analogous to the State and Federal income tax). These rates vary depending on the amount of money you make and your province of residence. Consider the overall marginal income tax rate 53.53%.
Is this function continuous on the domain of all possible household incomes?
Click here to see answer by ikleyn(52794) |
Question 1203719: Create an equation of a piecewise function that has the following properties:
- includes 4 different types of functions (e.g. linear, quadratic, exponential, square root)
- is continuous
- has limiting behaviour as x --> ± ∞, y --> + ∞
Click here to see answer by Edwin McCravy(20056)  |
Question 1203719: Create an equation of a piecewise function that has the following properties:
- includes 4 different types of functions (e.g. linear, quadratic, exponential, square root)
- is continuous
- has limiting behaviour as x --> ± ∞, y --> + ∞
Click here to see answer by greenestamps(13200) |
Question 1203719: Create an equation of a piecewise function that has the following properties:
- includes 4 different types of functions (e.g. linear, quadratic, exponential, square root)
- is continuous
- has limiting behaviour as x --> ± ∞, y --> + ∞
Click here to see answer by mccravyedwin(407)  |
Question 1203773: f(x) = x^2 + 5
a) f(-6) =
b) Find if f(x) = 14
c) f(x + h) =
d) Calculate: f(x + h) - f(x) over h
Can you please explain to me this homework question by showing the step-by-step calculations? Thank you!
Click here to see answer by Theo(13342) |
Question 1203907: a norman windo with a perimeter of 20 units has the shape of rectangle surmounted by a semi-circle. If its base is x units long and the height of the rectangle is y units long, write a mathematical model for its area in terms of x.
Click here to see answer by Theo(13342) |
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