Question

Use the table to answer the question.

This table shows the relationship between x and y defined by the given equation along with the corresponding points (x,f(x)) , where f(x) is the inverse of function x in terms of y.
y 3y−1=x
(x,f(x))

−2
−0.89
(−0.89,−2)

−1
−0.67
(−0.67,−1)

0 −1
(−1,B)

1 2 (2,1)

2 A
(A,2)

3 26 (26,3)

In order to graph a logarithmic function, a table has been created. The function has been rewritten in exponential form. What are the values for A
and B
?

(1 point)
A=
and B=

Answer 1

To solve for \( A \) and \( B \) in the given table, we start with the equation that defines the relationship between \( x \) and \( y \):

\[
3y - 1 = x
\]

We can rearrange this equation to express \( y \) in terms of \( x \):

\[
3y = x + 1 \implies y = \frac{x + 1}{3}
\]

Now we can use this equation to find \( B \) and \( A \).

**Finding \( B \):**

Using the point \( (−1, B) \):

\[
B = \frac{−1 + 1}{3} = \frac{0}{3} = 0
\]

So, we have:

\[
B = 0
\]

**Finding \( A \):**

Using the point \( (A, 2) \):

\[
2 = \frac{A + 1}{3}
\]

Now, we solve for \( A \):

Multiply both sides by \( 3 \):

\[
6 = A + 1
\]

Subtract \( 1 \) from both sides:

\[
A = 6 - 1 = 5
\]

So, we have:

\[
A = 5
\]

In summary, the values are:

\[
A = 5 \quad \text{and} \quad B = 0
\]