Question

f f(x) is parallel to the line mc001-1.jpg, which function could be f(x)?
mc001-2.jpg
mc001-3.jpg
mc001-4.jpg
mc001-5.jpg

Answer 1

I can’t see the images you referenced. Could you either upload them here or type the equations/describe the line and the 4 choices?

In the meantime, here’s how to decide, depending on what the question means:

1) If they mean “the graph of f(x) is parallel to the given line” (the entire graph is parallel)
- Find the slope m of the given line (pick two points on the line and compute Δy/Δx).
- A function whose entire graph is parallel to that line must be a linear function with the same slope m (i.e. f(x) = m x + b for some b). So among the choices pick the one with x-coefficient equal to m.

2) If they mean “the tangent to f(x) is parallel to the given line” (i.e. the curve has a tangent with that slope at some x)
- Find the slope m of the given line.
- Compute f '(x) for each candidate and solve f '(x) = m. If there exists an x where that holds, that function has a tangent parallel to the line.

If you upload the images or type the line (e.g. y = 2x − 1) and the four choices (paste the four functions), I’ll pick the correct one and show the work.