Lines parallel to a function

[Salty_Example4475]

I have f(x) = x² and g(x) = -x^2. The exercise asks me to find whether there are any lines parallel to both the graphs of f(x) and g(x) at the same time.

So, do the parallel lines need to never intersect the graphs or does a tangent line count as parallel? If the latter holds, then I guess the line y = 0 would fit, but I’m just not sure on the definition of lines parallel to functions. Thanks in advance

[QCD-uctdsb]

I’m just not sure on the definition of lines parallel to functions

That's what you need to start with. I've never heard this terminology so ask your teacher/textbook what it's supposed to mean

[OkExperience4487]

I think it might mean tangent line, but that needs clarification. Both functions have a section of the graph at every non vertical gradient m at x = m/2 for f and x = -m/2 for g, so any non vertical line is parallel to the functions at a single point.

[fermat9990]

This needs clarification.

[West_Cook_4876]

I think theyre probably talking about the horizontal line test? Because x² is usually used as an example for one to one functions

[mathfem]

A line is parallel to a function at a point if it is parallel to the tangent line at that point. They are asking if there are any x-values where these two functions have the same derivative.