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# How do you graph $y=\ln x-1$?

Last updated date: 14th Sep 2024
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Hint: We first try to plot the graph for $y=\ln x$. Then we find the graph for $y=\ln x-1$ by lowering the graph line of $y=\ln x$ by 1 unit. The lowering or ascending of the graph is totally dependent on the use of the constant 1 in the equation of $y=\ln x-1$.

Complete step-by-step solution:
We need to plot the graph of $y=\ln x-1$.
The usual common graph which is easier to plot on the graph is $y=\ln x$.
The graph is an increasing graph with range being $\left( -\infty ,\infty \right)$.
The domain for the graph $y=\ln x$ is $\left( 0,\infty \right)$.

Now depending on the above-mentioned graph, we are going to find the graph of $y=\ln x-1$
The change between $y=\ln x$ and $y=\ln x-1$ is that for a particular value of $x$, we are going to find the value of $y$ being 1 less than the previous value for $y=\ln x$.
This means that we are going to lower the graph with respect to the previous graph line which is for $y=\ln x$ at the time of changing the graph from $y=\ln x$ to $y=\ln x-1$.
The domain for the graph $y=\ln x-1$ is $\left( 0,\infty \right)$.
The range for the graph $y=\ln x-1$ is $\left( -\infty ,\infty \right)$.

Note: We need to be careful about the change from $y=\ln x$ to $y=\ln x-1$. The lowering or ascending of the graph is dependent on the constant value that is being added. If the value is positive then graph ascends and if the value is negative then it descends.