Question

The characteristics of a function in the form
y
=
a
⋅
b
x
+
c
are described below.

The function increases in value as the values of
x
increase.
The function has a
y
-
intercept of 6.
Which table could contain pairs of
x
-
and
y
-
values for this function?

Answer 1

I don’t see the answer choices/tables — could you paste them?

Meanwhile, here is a quick way to check each table:

1. A y‑intercept of 6 means y(0)=6, so the table must have the pair x=0, y=6. If it doesn’t, reject that table.
2. Write y = a·b^x + c. From x=0 we get a + c = 6.
3. For two other x values (say x=1 and x=2) let y1, y2 be the y’s. Then y1 − c = a·b and y2 − c = a·b^2. So
(y2 − c)/(y1 − c) = b and (y1 − c)/(6 − c) = b. Equate them to test consistency:
(y2 − c)(6 − c) = (y1 − c)^2.
4. Solve that equation for c (it’s a quadratic). If you get a real c that makes a = 6 − c and b = (y1 − c)/a both valid and (a·ln b) > 0 (so the function increases), the table can be from such a function.

If you post the tables, I’ll apply these steps and pick the correct one.