Match the function with its graph. [The graphs are labeled (a), (b), (c), and (d).] (GRAPH CANNO

Match the function with its graph. [The graphs are labeled...

Key Concepts

Reflection Transformation

Multiplying a function by -1 reflects its graph across the x-axis. In the case of f(x) = -ln x, this transformation turns the increasing behavior of ln(x) into a decreasing one while keeping the original domain (x > 0) and the vertical asymptote at x = 0 intact.

Natural Logarithm Function

The natural logarithm function, ln(x), is defined for x > 0. Its graph is characterized by a steady increase as x increases, passes through the point (1, 0), and has a vertical asymptote at x = 0.

Transcript

00:01 According to the question we need to match the given function with the correct graph and the function given to us is that f of x is equal to minus of natural log of minus x.

00:18 Now we know that the standard form is simply natural log of x.

00:25 Now we also know that when a point is being reflected along the y axis then it becomes minus xy and when this point will be reflected along the x axis then we'll get minus x minus y now since in the given function there are two negatives first negative is with the x coordinate and the next one is the value of fx so, what we need to do is, first of all, we need to plot the graph of the original function.

01:12 Then we need to plot the graph when the given function, the standard function is being reflected along the y -axis.

01:19 And finally, we need to plot the graph when it is being reflected along the x -axis.

01:25 So let us see what are we going to get.

01:27 Now before plotting, let us understand when this function is going to be reflected along x -axis, so what can we say that f of x will become equal to minus natural log of? now over here we will not put a minus sign outside the natural log.

01:49 Since it's being reflected along the y axis, so the negative sign will go inside and we need to be careful with this.

01:55 So it will become f of x will be equal to simply natural log of minus x.

02:00 Now for the next step we are going to get that the reflection of this function, if f of x is natural log of minus x, then this function on reflection will now become minus natural log of minus x...

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