Question

For this tangent line approximation question, my answer is D. 4. Is my work correct?

Answer 1

Yes choice D is the correct answer. Nice job.

If you wanted, you can simplify the linear approximation L(x) 
L(x) = f(a) + (x-a)*f'(a)
L(x) = f(-0.5) + (x-(-0.5))*f'(-0.5)
L(x) = 2 + (x+0.5)*4
L(x) = 2+4x+2
L(x) = 4x+4

Then plug in x = 0
L(x) = 4x+4
L(0) = 4(0)+4
L(0) = 4

But your method is a shorter route.