Question

Which graph represents the solution set y > −negative 5 over 2x + 2?
A
X; Y;
B
X; Y;
C
X; Y;
D
X; Y;

Answer 1

I’m missing two things before I can pick A–D: (1) the exact algebraic inequality (the text is ambiguous), and (2) the four graphs (or a description of them). Can you confirm whether the inequality is

a) y > −5/(2x + 2) or
b) y > 5/(2x + 2) (or something else)?

If it is y > −5/(2x + 2), here are quick tests you can use to choose the correct graph:

- The boundary curve is the rational function y = −5/(2x+2). The vertical asymptote is x = −1 and the horizontal asymptote is y = 0.
- Because the inequality is strict (>), the boundary should be dashed (not solid).
- Pick an easy test point, e.g. (0,0). For y > −5/(2·0+2) = −5/2 = −2.5, (0,0) satisfies the inequality (0 > −2.5). So the correct graph must have the point (0,0) in the shaded region (above the dashed hyperbola).
- The curve branches: left of x = −1 the branch is above the x-axis; right of x = −1 the branch is below the x-axis.

If it is y > 5/(2x + 2), same asymptotes (x = −1, y = 0) but the hyperbola is reflected vertically; test (0,0) gives 0 > 2.5 false, so (0,0) would be outside the shaded region.

Send the exact inequality (a or b) and either the images or a brief description of each choice (where the asymptotes are, whether boundary is dashed/solid, and whether (0,0) is shaded) and I’ll tell you which letter is correct.