ToughSTEM
ToughSTEM
A question answer community on a mission
to share Solutions for all STEM major Problems.
Cant find a problem on ToughSTEM?
0
A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one.

f (x) = x^2 - 2*x

Found in Stewart 7th Ed Section 6.1 #9
Edit
Community
1
Comment
Solutions
0
A one to one function is one where every x value has a unique f(x) value.

There are two ways to solve this.

1) By guessing and noticing that both f(0) and f(2) = 0 - which means the function is not one to one

2) or the better way - systematically.
f (x) = x^2 - 2*x
y = x^2 - 2*x

Complete the square to see the problem more clearly (to put it into standard parabolic form)

y + (-2/2)^2 = x^2 - 2*x + (-2/2)^2

Now simplify

y + 1 = x^2 -2x + 1
y + 1 = (x-1)^2

Put into standard form

y - (-1) = (x-1)^2

This tells us that this equation is a parabola with a vertex at -1,-1

As parabolas are not one-to-one functions, this function is not a one to one function.
Edit
Community
1
Comment
Close

Choose An Image
or
Get image from URL
GO
Close
Back
Close
What URL would you like to link?
GO
α
β
γ
δ
ϵ
ε
η
ϑ
λ
μ
π
ρ
σ
τ
φ
ψ
ω
Γ
Δ
Θ
Λ
Π
Σ
Φ
Ω
Copied to Clipboard

to interact with the community. (That's part of how we ensure only good content gets on ToughSTEM)
OR
OR
ToughSTEM is completely free, and its staying that way. Students pay way too much already.
Almost done!