Question

Given the graph below, determine the values for a and b in the equation y=blog_3(x+a) . If a value is a non-integer then type it as a reduced fraction.vert asymp at x=-4.as x goes to -4,f(x) goes to infinity.as x goes to infinity f(x) goes to -infnity. (5,4) is on the graphThe value for a is AnswerThe value for b is Answer

Answer 1

Given the equation:

$y=b\log _3(x+a)$

Let's find the values of a and b using the given graph.

Since the curve faces up, the value of b will be less than 1.

We have:

Vertical Asymptote at x = -4

Equate to zero:

x + 4 = -4 + 4

x + 4 = 0

Thus, we have:

$y=b\log _3(x+4)$

Now, take the point:

(x, y) ==> (5, -4)

Input the values for x and y, then solve for b:

Where:

x = 5

y = -4

$\begin{gathered} -4=b\log _3(5+4) \\ \\ -4=b\log _3(9) \\ \\ b=\frac{-4}{\log _39} \\ \\ b=\frac{-4}{\log _3(3^2)} \\ \\ b=\frac{-4}{2\log _33} \\ \\ b=\frac{-2}{\log _33} \\ \\ b=-\frac{2}{1} \\ \\ b=-2 \end{gathered}$

Therefore, the equation is:

$y=-2\log _3(x+4)$

• The value for a is , 4

,

• The value for b is , -2