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Match the logarithmic function with its graph.\begin{equation}\begin{array}{ll}{\text { (a) } f(x)=\log _{2} x} & {\text { (b) } f(x)=\log _{2}(-x)} \\ {\text { (c) } f(x)=-\log _{2} x} & {\text { (d) } f(x)=-\log _{2}(-x)}\end{array}\end{equation}

$$\begin{array}{ll}{(a) \rightarrow I I I} & {(b) \rightarrow I I} \\ {(c) \rightarrow I} & {(d) \rightarrow I V}\end{array}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

McMaster University

Harvey Mudd College

Baylor University

Lectures

01:32

In mathematics, the absolu…

01:11

00:51

Match the logarithmic func…

02:32

Graph each logarithmic fun…

00:20

02:47

00:44

00:37

01:34

Match the function with it…

00:38

00:52

00:22

So here we are, analyzing the groves off all the functions. So let's look at a If we use a small table for this graph, then four X equal to two, all right where X is equal to two. Then why all the ethics? So if this is the ethics and that's eggs, then I'm going to have a coordinate at one and two. What and let's see which way does go if X is 1/2? So that's approximately. They for eggs are half then that if X will be negative one just to get a few village and just to get a feeling off what it's going to look like. So let's go. But bigger. What if X is full right for X equal to four? So look at this. I just use a small table. I've put X equal to 1/2 and I did. If X is the equal to negative one. If I make eggs equal to two, then if off X is equal to one, and if I put X equal to four, then I will get my if eggs equal to two. So it's going up the right, so those are approximate. There's just a few values on this growth just to get an indication off what the growth, which direction the growth will go in and R C. That's approximately going that way. So which option is this? This is the option number three. So for a I choose Option three, let's look at B. What happens at B? Yeah, it's still the same growth as in a Except for that X, that becomes negative. So if we think of translations, what type of translation is it where the eggs becomes negative for an ex value to change? It is a reflection over the if eggs excess. So, in other words, it's going to go this way. We don't have the value off. I'll have some very off negative, too. And one day, fool my co ordinates for just and a coup, a pair of coordinates. And this thing is option number two, right? So let's look at see what happens at sea, See is the function that was in a butt. The whole function becomes now becomes negative so that in its on, it's a reflection about the X axis. So we'll take the grove off, eh? And reflected about the eggs access and we will end up with this fool, right? We in this case will have too and negative one day. So this is then option one, then for the last one in D. So for D, it has reflected the function off has reflected in the Y in the X End, the y axis. So it is the reflection of being see together. So let's reflect it according to be in the y axis first and then in there eggs exists and we will end up with a function looking like option full. So that is the option 4 40

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