The graph of the logarithmic function that passes through (-2,-2) and (1,0) is .
Suppose that the function is
Then there are two observations that we must consider from the figure
- The graph must pass through (-2,-2) and (1,0)
So,
And,
Observe the figure given below we see that the graph of
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 moves left and
When we decrease d then the graph moves down.
That makes the graph required to be .
Hence, the graph of the logarithmic function that passes through (-2,-2) and (1,0) is .
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