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Question

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

Erna Bisschoff · Accepted Answer

So here we are, analyzing the groves off all the functions. So let&#x27;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&#x27;s eggs, then I&#x27;m going to have a coordinate at one and two. What and let&#x27;s see which way does go if X is 1/2? So that&#x27;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&#x27;s going to look like. So let&#x27;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&#x27;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&#x27;s going up the right, so those are approximate. There&#x27;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&#x27;s approximately going that way. So which option is this? This is the option number three. So for a I choose Option three, let&#x27;s look at B. What happens at B? Yeah, it&#x27;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&#x27;s going to go this way. We don&#x27;t have the value off. I&#x27;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&#x27;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&#x27;s a reflection about the X axis. So we&#x27;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&#x27;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

Ankit Gupta · Answer

we are going to use the bordering properties to solve some that look to the base A. When equals zero no to the base, a sequence for long to the base A things to be country on. Anything is to love to the base A B will speak. We are given for a look to the base. Three, three days to seven. This is equal to seven as treason to 70. Then we are given up to the base for 64. This can be really as no baseball. Four days to three, Penza answers. Three. That we have a look to the base. Five. One training by which can religion as look to the base price finalise to tree, which again has Toronto asked me.

Liuxi Sun · Answer

my breath, Nick. Function of X equals luck, ace to affects and were asked a graph it. So first we want to do is let&#x27;s replace f of X as why to make things look a little bit off more familiar and easier to, uh, you Valley. Wait. So once we have this, what we&#x27;re gonna want to do is now converted into exponential for so we take the base, which is to raise it to the power, Which is why I said equal to the argument which is X once you have that is so much easier to plug and chug out some data points to plus. So let&#x27;s to a random assortment of why values they too? Negative ones 01 and two. So to race to the negatives to power is negative is 1/4 to race the native one powers 1/2 and to raise to the zero power is one to race. The one power is too to raise to the second power is for So now we can begin plotting. So when X equals 1/4 by equals negative too. When I see it was 1/2 y goes one and X equals one like was zero to one for to Now we&#x27;re seeing that shape for like that, and we can expect that this, um the graph will not exceed the Y axis. It will not exceed into go into the xnegative X valleys because the domain of all of the general lager thank function is always positive. Real numbers. So positive riel, positive numbers for ex. And why can be any number between negative infinity and infinity? So it could be positive or negative ends through this method just by applauding down a few data points and converting the lager that locker reflect function into an exponential one. We can thus rough out easily, but the shape will look like roughly.

Katelyn Chen · Answer

for this question were given the function F X. It&#x27;s equal to natural log of X minus two. So we knew that, too causes Augusta shift right by two units, and we noticed that the graph that justice is graft to

Liuxi Sun · Answer

you were given a function f of X equals log based 1/2 of X. So now let&#x27;s do a few things for So let&#x27;s change. The effort acts to why so it&#x27;s easier to understand and two so we can plot more easily on the X my cornea graph. And then let&#x27;s change 1/2 into suits the negative one power. And this will help at the next step when we convert the lager, think function into exponential form. So for this we take the base, which is to the night of one, and we multiply. It reads. Used the race to the power bi. When you raise on exponential exponent exponents to another power, then you essentially multiply them together. It&#x27;s one of the exponential rules, so you get negative, too. Why equals X? So now let&#x27;s assign a few values for what makes to native 101 and two. So when y is equal to negative two than its rate, it&#x27;s two to the second power. So that&#x27;s four. When y zero to negative one that&#x27;s 2 to 1, which is to and to to the zero is one to to the negative one is 1/2 and two to the on for two to the mega for power or noticed. Second power is 1/4 14 How we can begin plotting these samples So X equals four by this negative too. X equals two. And why equals XY was fun. Why zero 1/2 one? For So now we&#x27;re starting to see that she like that. And the reason why the shape is facing upwards like that is because when we look at this a about you, the value over here we see that a value to to to the negative one is equal to 1/2. And if a is less than one, but they also must be greater than zero. If this is true, then the graph shape would look something similar to that. So we can verify that this is indeed roughly the shape of the graph of y equals log base, 1/2 of X

Ankit Gupta · Answer

given the do craft and we have to match them with the function. F X equals low enough. X minus two. There are two approaches to it. The first approaches. By placing in the point, we&#x27;ll start with lugging and see X equals three. That case is a 43 has long with that zero. The point is to Tacoma zero, which means the second craft marches who We can also know it a quicker way to solve the Cyprus direction. As therefore, this function. ASEM dude is at X equals two. So we identify the excepto I liked it.

Problem

The natural logarithmic function $f(x)=\ln x$ has…

Problem 4 Medium Difficulty

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}

Answer

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

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

Algebra and Trigonometry

Grace H.

Alayna H.

Kayleah T.

Caleb E.

Absolute Value - Example 1

Absolute Value - Example 2

James Stewart, Lothar Redlin, Saleem WatsonAlgebra and Trigonometry

Grace H.

Alayna H.

Kayleah T.

Caleb E.

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

James Stewart, Lothar Redlin, Saleem Watson

Algebra and Trigonometry