Use the table to answer the question.

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:

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