Problem

$93-94=$ Inverse Functions A function $f(x)$ is g…

Problem 92 Easy Difficulty

$91-92$ . Family of Functions A family of functions is given.
(a) Draw graphs of the family for $c=1,2,3,$ and $4 .$ (b) How are
the graphs in part (a) related?
$$f(x)=c \log x$$

Answer

As we can see in the picture above the graph of each function for $c=2,3,4$
is the same as the graph of $f_{1}(x)=\log (x)$ but vertically streched by a
factor of $c .$

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Algebra

Algebra and Trigonometry

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

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Video Transcript

So I've graft this function here with differing values of C. So I've graphed c is equal to C is equal to one in red. I've graphed si is equal to two in blue he is equal to two and blue Si is equal to three angry and C is equal to four in black And so you might think that as we increase See that we're that we're moving this graph upward. You might think it's easy to think that you were just moving the graph upward. But what we want to notice here is that that let's look at our intercepts here. Well, with C is equal to one we have we have this intercept at X is equal to one that c is equal to two. We're doubling one. So we're having the the X intercepts Our interceptors one and so three is is about 1.5 more than two. So instead of having this, this would be 0.75 or rather and then somewhere around 0.75 And so when we get to see is equal to four, si is equal to four. This is 1/4 uh, one. So there should be 1.25 to be one point or this should be 1.0.25 not 1.25 This is 1/4 of one. So this is 10.25 Let's label these 0.25 this is 0.75 Or rather, this would be this would be one divided by three This 12.33 So I misspoke when I said 0.3 point 75 is actually 1.33 So this is 0.5. This is labeled and this is this is one. So So we're not actually increasing this graph for shifting this graph upward. What we're actually doing is is shrinking. This graph were shrinking it to the left. So we're actually imagine compressing the graph so so that as see increases We go from red to blue who are shrinking this and from blue to green work in shrinking and then the same thing with green to black. So we notice our pattern here as as C increases SC increases our graph or our function shrinks shrinks. And so this is what we've noticed when we graft this. This is our solution

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