Question

True or False. This graph represents the function y = x −1
.

Show your work.



(1 point)
Responses

True
True

False

Answer 1

I can’t see the graph you mean. Please upload or describe it.

Meanwhile, here are quick ways to decide and how to "show your work" depending on which equation you meant:

1) If the equation is y = x − 1 (a line):
- Pick two clear points on the graphed line, e.g. (x1,y1) and (x2,y2).
- Compute slope m = (y2 − y1)/(x2 − x1). For y = x − 1 you should get m = 1.
- Find the y‑intercept (value of y when x = 0). For y = x − 1 the intercept is −1.
- If slope = 1 and y‑intercept = −1, the graph matches y = x − 1 (True). Example: points (0,−1) and (1,0) give slope (0 − (−1))/(1 − 0) = 1 and intercept −1 → y = x − 1.

2) If the equation is y = x^(−1) = 1/x (a reciprocal/hyperbola):
- The graph is a rectangular hyperbola with vertical asymptote x = 0 and horizontal asymptote y = 0, and it will not be a straight line.
- Pick points and check: for y = 1/x, points like (1,1) and (2,0.5) should lie on it. If the graph is a curved hyperbola, then it does NOT represent y = x − 1 (False).

Send the graph (or describe a couple of points on it and any asymptotes) and I’ll tell you True or False and show the work.