Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 1195886: Read the description of the below relation and decide whether it is a function.
An engineer tests different models of cars to determine which car has the best mileage. He records the miles per gallon of each model of car.
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Question 1195885: Read the description of the below relation and decide whether it is a function.
A teacher records the number of A's that a class earns on a test throughout the year.
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Question 1195883: Read the description of the below relation and decide whether it is a function.
The number of inches, I, that Peter grows each year, y.
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Question 1195884: Read the description of the below relation and decide whether it is a function.
Steven does yard work for his neighbors. He earns $10 for every lawn that he mows plus $3.50 for raking leaves.
Click here to see answer by ikleyn(52748)

Question 1195900: Each set of ordered pairs represents a function. Write a rule that represents the function.
1. (2,10), (4,20), (5,25), (7,35), (9,45)
2. (2,5), (4,9), (5,11), (7,15), (10,21)
The answer I got the the first set of ordered pairs was f(x) = 5x, and for the second pair of ordered pairs, the answer I got was f(x) = 2x+1. Are my answers correct?
Click here to see answer by ikleyn(52748)

Question 1195899: Each set of ordered pairs represents a function. Write a rule that represents the function.
1. (2,10), (4,20), (5,25), (7,35), (9,45)
2. (2,5), (4,9), (5,11), (7,15), (10,21)
The answer I got the the first set of ordered pairs was f(x) = 5, and for the second pair of ordered pairs, the answer I got was f(x) = 2x+1. Are my answers correct?
Click here to see answer by ikleyn(52748)

Question 1195889: A is a nonempty set. The empty relation ∅ is a relation on A.
Is the relation R=∅ invertible in (R(A),o)
a. No. For all S ∈ R(A), ∅o S= ∅
b. Yes. Its inverse is ∅
Click here to see answer by ikleyn(52748)

Question 1195917: Determine whether the relation is a function.
t{(4,8),(20,-9),(36,8),(4,6),(50,6)}
Click here to see answer by MathLover1(20849)

Question 1195917: Determine whether the relation is a function.
t{(4,8),(20,-9),(36,8),(4,6),(50,6)}
Click here to see answer by math_tutor2020(3816)

Question 1195928: How would you find the domain of the function y=√tanx I believe that all I would have to do is find when the input of tanx causes the answer to be negative like 3pi/4 is that correct?
Click here to see answer by ikleyn(52748)

Question 1195941: I am coming up with -x^2+5x-7 for this problem
Given f (x) = 5x - 4 and g (x) = x2 + 3, find (g - f )(x). Simplify when possible.
But that is not one of the choices. Can you please help me?
Click here to see answer by Alan3354(69443)

Question 1196042: Find the domain for the function.
f(x)=x\7x^2+5
Click here to see answer by MathLover1(20849)

Question 1196071: The dimensions of a rectangular piece of paper ABCD are AB= 10 and BC = 9. It is folded so that corner D is matched with point F on edge BC. Given that length DE= 6, find EF,EC,FC, and the area EFC.
The lengths EF, EC, and FC are all functions of the length DE. The area of triangle EFC is also a function of DE. Using X to stand for DE, write formulas for these four functions,
Find the value of X that maximizes the area of triangle EFC.
Diagram link:
https://math.stackexchange.com/questions/2421004/areas-in-a-folded-sheet-of-paper

Click here to see answer by greenestamps(13195)

Question 1196079: Write a function rule that represents the sentence.
8 fewer than p times 3 equals x.

Click here to see answer by ikleyn(52748)

Question 1196082: Write a function rule that represents the sentence.
The ratio of a to 5 equals b.
Click here to see answer by josgarithmetic(39613)

Question 1196082: Write a function rule that represents the sentence.
The ratio of a to 5 equals b.
Click here to see answer by ikleyn(52748)

Question 1196097: f(x) = x2 − 2x + 4, (f(7 + h) − f(7))/ h , h ≠ 0
find the difference quotient and simplify your answer
Click here to see answer by MathLover1(20849)

Question 1196096: f(x) = x2 − 2x + 4, f(7 + h) − f(7) h , h ≠ 0
find the difference quotient and simplify your answer.
Click here to see answer by MathLover1(20849)

Question 1196124: The point (0,1) belongs tk the function.
a. f(x)=x²+1
b. f(x)=x²-2
c. f(x)=x³+1
d. f(x)=x+1

Click here to see answer by josgarithmetic(39613)

Question 1196164: Direction: Represent a real-life situations using piece-wise function.
1. Provide a real-world example or scenario that can be expressed as a relation that is not a function.
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Question 1196172: A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b

Click here to see answer by MathLover1(20849)

Question 1196172: A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b

Click here to see answer by josgarithmetic(39613)

Question 1196172: A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b

Click here to see answer by math_tutor2020(3816)

Question 1196172: A function is defined by g:x=ax²+bx+2 where a and b are constants. If g(-2)=6 and g(3)=11, Find the values of a and b

Click here to see answer by MathTherapy(10549)

Question 1196196: Express the domain of 𝑓(𝑥) = 𝑔1(𝑥) + (𝑔2(𝑥))^2 + √𝑔3(𝑥) in terms of the domains of 𝑔1, 𝑔2 and 𝑔3.
Click here to see answer by ikleyn(52748)

Question 1196203: Hello,
I have completed these exercises about finding the domain and range. Are they correct?
3. y = 20 - 2x^2
Domain: (-∞, +∞)
Range: (-∞, 20)

4. y = 25(-7x-4)^64
Domain: (-∞, ∞)
Range: (0, ∞)
Thank you so much,
Fernando
Click here to see answer by ikleyn(52748)

Question 1196242: Given the function y=h(x) defined by the set of ordered pairs {(-2,3), (-1,0), (1,0), (2,3), ..., (3,8)}, find h(3)+h(10).
Show full solution, thanks!!
Click here to see answer by greenestamps(13195)

Question 1196269: If and , find the value of g(0).
Click here to see answer by ikleyn(52748)

Question 1196269: If and , find the value of g(0).
Click here to see answer by MathLover1(20849)

Question 1196268: If and f(x) is the inverse of g(x), determine the value of f(-1).
Sidenote: If you could also explain to me what the inverse of a function means and what it implies for this question specifically, I would really appreciate that :) thank you so much!!
Click here to see answer by josgarithmetic(39613)

Question 1196271: Hi, I need help understanding this question and how to answer it. Thank you in advance math tutors!
Given a function f of a real variable that satisfies the equation defined by for all real x, determine f(x) in terms of x.
Click here to see answer by MathLover1(20849)

Question 1196357: Assume the number of U.S. households with land-line phones stood at 45 million at the beginning of 2014 and was projected to decline at the rate of 1.5 million households per year for the next 8 years.
Find a linear function f giving the projected U.S. land-line phone households (in millions in x year ), where x =0 corresponds to the beginning of 2014.
f (x) =

What is the projected number of U.S. land-line phone households at the beginning of 2019?
Answer =
million households
Click here to see answer by josgarithmetic(39613)

Question 1196402: find the domain and range of function f(x)=3x-2 and sketch a graph for this

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Question 1196402: find the domain and range of function f(x)=3x-2 and sketch a graph for this

Click here to see answer by math_tutor2020(3816)

Question 1196464: Find a formula for the inverse of the function.
f(x) = 6x − 1/2x + 9
f −1(x) = (f inverse of x).

Click here to see answer by josgarithmetic(39613)

Question 1196464: Find a formula for the inverse of the function.
f(x) = 6x − 1/2x + 9
f −1(x) = (f inverse of x).

Click here to see answer by greenestamps(13195)

Question 1196463: Find a formula for the inverse of the function.
f(x) = 6 − x2(x raised to the power of 2), x ≥ 0
f −1(x) =

f(x) = 6 − x2, x ≥ 0
f −1(x) =

Click here to see answer by josgarithmetic(39613)

Question 1196463: Find a formula for the inverse of the function.
f(x) = 6 − x2(x raised to the power of 2), x ≥ 0
f −1(x) =

f(x) = 6 − x2, x ≥ 0
f −1(x) =

Click here to see answer by math_tutor2020(3816)

Question 1196481: If f, g, and h are functions, and m and b are real numbers such that , for all x, find the values of m and b.
Click here to see answer by josgarithmetic(39613)

Question 1196480: if and , find the value of g(2).
Click here to see answer by ikleyn(52748)

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