Question

The shape of the graph \(\ln 1 \rightarrow t\) is (A) straight Line (B) Parabolic curve (C) Hyperbole curve (D) random shape curve

Short answer

The shape of the graph $\ln 1 \rightarrow t$ is a straight line because the natural logarithm of 1 is always 0, and the function can be rewritten as $0 \rightarrow t$. This results in a horizontal line along the t-axis. Therefore, the answer is (A) straight Line.

Step-by-step solution

Recognize the function

We have the function \(\ln{1} \rightarrow t\). As mentioned before, the natural logarithm of 1 is always equal to 0. So, this function can be rewritten as \(0 \rightarrow t\).

Evaluate the function

Since \(\ln{1} = 0\), every input (\(t\)) will generate the same output, which is 0. This function can be viewed as \(y = 0 \rightarrow t\). In this equation, no matter what \(t\) is, the result will always be 0 for \(y\).

Determine the graph shape

As no matter the value of \(t\), the result is 0, the graph will be a horizontal line along the \(x\)-axis (t-axis). This means that the shape of the graph is a straight line. The correct answer is: (A) straight Line