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?


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Answer 1

I can do this, but I can't see the four images you attached. Please either

- upload the images again, or
- copy the four tables here as text (list the x and y pairs for each).

To save you time, here is a quick checklist you can use to eliminate/confirm each table yourself:

1. Because y = a·b^x + c and the y-intercept is 6, you must have y(0) = a + c = 6. If a table does not have a point with x = 0 and y = 6, that table cannot be the function.

2. If a table does include the points (0, 6), (1, y1) and (2, y2), compute
b = (y2 − y1) / (y1 − 6).
- If b ≤ 0 or b = 1 the function is not an increasing exponential of the required form.
- For the function to increase you need b > 1 and a = 6 − c > 0 (so c < 6).

To find c (if you want to verify):
c = (y1 − 6b) / (1 − b).
Then a = 6 − c; check a > 0.

3. If the table does not include x = 0 you can still test three distinct rows (x1,y1), (x2,y2), (x3,y3): the values y − c must form a geometric sequence (ratios equal), so solve for c and b from the three points (or use two ratios equality to eliminate c). If the resulting b > 1 and a = 6 − c > 0, the table could match.

Send the actual table values and I'll check each one and give the correct choice.