Question

Please Answer Asap!!! Write the equation based on the graph of the following base 2 logarithmic function:

Answer 1

The graph of the logarithmic function that passes through (-2,-2) and (1,0) is $\log_2(x+3)-2$.

Suppose that the function is

$f(x)=\log_2(x+c)+d$

Then there are two observations that we must consider from the figure

1. The graph must pass through (-2,-2) and (1,0)

So,

$-2=\log_2(-2+c)+d$

$\implies -2+c=e^{-2-d} ...~...~(1)$

And,

$0=\log_2(1+c)+d\\\implies 1+c=e^{-d} ~...~...~(2)$

Observe the figure given below we see that the graph of

$\log_2(x)$ passes through (1,0) but does not pass through (-2,-2) and the graph is to the right of (-2,-2) hence, we need the graph to move left.

When we increase c the graph  $\log_2(x+c)+d$  moves left and

When we decrease d then the graph  $\log_2(x+c)+d$  moves down.

That makes the graph required to be   $\log_2(x+3)-2$.

Hence, the graph of the logarithmic function that passes through (-2,-2) and (1,0) is $\log_2(x+3)-2$.

Learn more about logarithms here-

brainly.com/question/20785664

#SPJ10