Question

Which of the following functions are one-to-one? Select all that apply (theres three right answers)

a) f(x)= x-1/3x+3
b) f(x) = srt5x+9
c) f(x) = 7/4x^2
d) f(x) = 1/2x^3
e) f(x) = 3x^4+7x^3

I don't really understand what one-to-one means. So i need help please. Thanks.

Answer 1

1-1 means that
(a) no two values of x map to the same value of y (horizontal line test)
(b) each value of x has only one value of y (vertical line test)
That is, each and every x maps to a unique value of y.

in other words, the function is either always increasing (like y=x or logx)
or always decreasing (like y = -x^3 or y = e^-x)

even-order polynomials always open up or down, but they always turn back on themselves. They fail the horizontal-line test.

So, what do you think? If in doubt, graph the function.

Answer 2

Um, I graphed them, and I took an educated guess based off of what you said and picked b, d, and e...not sure if this correct though

Answer 3

b and d yes
e is 4th degree, so it will look kind of like a parabola, maybe with a bump at the bottom. If you picked e, you didn't graph it very well.

There are lots of online graphing sites where you can check your functions.

Answer 4

I used desmos, and graphed them. Since it wouldnt be e, would it be a then?

Answer 5

yes, a will work, if you exclude x = -1 from the domain, where f(x) is undefined.

Answer 6

Thank you :))

Answer 7

1. A, B, D
2. A
3. B
4. A

Answer 8

hwiyoung is right!

Answer 9

vouch

Answer 10

hwiyoung is correct

Answer 11

hwiyoung right as of feb 26 2022 on 2.4.7 quick check connexus

Answer 12

hwiyoung is still correct..

Answer 13

1. a: f(x)=(x-1)/3x+3 ,
b: f(x)= sqrt5x+9 ,
d: f(x)= (1/2)x^3

2. a: f^-1(x)=(x-8)^3 +2

3. b: this is a one to one function because there is no horizontal line that would intersect the graph of the function more than once.

4. a: domain - (-infinite, 0)U(0, infinite)
range - (-infinite, -2/3)U(-2/3, infinite)

100% - 4/4 as of sept 2nd, 2022.

Answer 14

Jake en- is 100% correct