borders/functions breakpoints

[wizardhat112]

I can't figure out with what to start i'm stuck in start. (can someone help me with start?)

. . . . .\(\displaystyle y\, =\, \begin{cases}1 & \mbox{ if }\, x\, \leq\, 2\\ \log_2(x) & \mbox{ if }\, 2\, <\, x\, <\, 4 \\ 5\, -\, x & \mbox{ if }\, x\, \geq\, 4 \end{cases}\)

Here is example what i have found

. . . . .\(\displaystyle f(x)\, =\, \begin{cases}2\, -\, x & \mbox{ if }\, x\, \leq\, 0\\ \cos(x) & \mbox{ if }\, 0\, <\, x\, < \, \dfrac{\pi}{2} \\ 0 & \mbox{ if }\, x\, \geq\, \dfrac{\pi}{2} \end{cases}\)

They are same?

because one has y=, but example what i found has f(x)= , does it make any difference???

 

[stapel]

I can't figure out with what to start i'm stuck in start. (can someone help me with start?)

Since you're provided no instructions or actual question, there is nothing to do. Until we receive that information, we cannot advise you on how to get started. Sorry.

. . . . .\(\displaystyle y\, =\, \begin{cases}1 & \mbox{ if }\, x\, \leq\, 2\\ \log_2(x) & \mbox{ if }\, 2\, <\, x\, <\, 4 \\ 5\, -\, x & \mbox{ if }\, x\, \geq\, 4 \end{cases}\)

Here is example what i have found

. . . . .\(\displaystyle f(x)\, =\, \begin{cases}2\, -\, x & \mbox{ if }\, x\, \leq\, 0\\ \cos(x) & \mbox{ if }\, 0\, <\, x\, < \, \dfrac{\pi}{2} \\ 0 & \mbox{ if }\, x\, \geq\, \dfrac{\pi}{2} \end{cases}\)

They are same?

because one has y=, but example what i found has f(x)= , does it make any difference?

You're in calculus, which means you've taken algebra, which means that you've studied function notation. (To refresh, try here.) As you'd learned there, yes, "y" and "f(x)" generally indicate the same thing. Also, yes, these are both piecewise functions.

When you reply with the instructions and any other information on this exercise, please also include a clear listing of your thoughts and efforts so far. Thank you!

 

[wizardhat112]

Sorry forgot about task "Detect function break points , and its type, draw function graph."

And how this type of exercise are named in english? like sinusoidal function , i can't find name anywhere for it?


To what thread i must move this topic i don't really understand?

 

[stapel]

Sorry forgot about task "Detect function break points , and its type, draw function graph."

The break points are the points (the x-values) at which the definition of f(x) changes. As for "type", you'll have to tell us the options your book has provided, and their definitions. To graph, just do the usual algebra.

 

[wizardhat112]

Is this right so far?

 

[stapel]

Why are you taking limits? I don't understand the relevance...?

Also, what are the "types" that your book (or instructor) defined?

What "breakpoints" did you find (by copying from the function definition)?

Where are you stuck in graphing the constant function, the linear function, and the log function?

Please be specific. Thank you! ;-)