Question

Which table represents the graph of a logarithmic function in the form mc029-1.jpg when mc029-2.jpg?
mc029-3.jpg
mc029-4.jpg
mc029-5.jpg
mc029-6.jpg

Answer 1

I can do this, but I can’t see the mc029-*.jpg images you referenced. Please either upload the images or type the function shown by mc029-2.jpg and the four candidate tables (the x and y pairs) from mc029-3..6.jpg.

To help you pick the correct table, here’s a short checklist you can use (and the algebra to verify):

1. Recognize the general transformed logarithm:
y = a·log_b(x − h) + k
- Vertical asymptote is x = h (so any valid table must have x > h).
- x-intercept (y = 0) occurs at x = h + b^(−k/a).

2. Use two known points (x1,y1) and (x2,y2) from a candidate table to check consistency:
- They must satisfy x1 > h and x2 > h.
- (x2 − h)/(x1 − h) = b^{(y2 − y1)/a}.
- If a = 1 and k = 0, then when y increases by 1, x − h should be multiplied by b.

3. Quick sign/shape checks:
- If a>0 and b>1 the curve increases (y grows as x increases).
- If a>0 and 0<b<1 the curve decreases.
- If a<0 the graph is flipped vertically (increasing ↔ decreasing).

Example: if the graph shows a vertical asymptote at x = 2 and points (3,0), (5,1), (9,2), that matches y = log_2(x − 2) because for y increments of 1 the (x−2) values are 1,2,4 (each multiplied by 2).

Send the function/graph image and the four tables (or type the table rows) and I’ll check them and tell you which one matches.