Question

Math Question! I have quite a few to post so just hang with me! :) I'll just post one at a time tho! I'm really not understanding this unit. :P

Answer 1

Still need help on this?

Answer 2

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
Still need help on this?
\(\color{#0cbb34}{\text{End of Quote}}\)
Yes please.

Answer 3

Okay, so since we are adding 1/2, we are shifting 1/2 units up.
Now for the second part.
\[f(\theta)=\tan(3\theta-210)+1/2\]
\[f(\theta)=\tan(3(\theta-70))+1/2\]
So it would be 70 degrees to the left, because we measure angles from the positive x-axis and move counter-clockwise,

These are my initial thoughts on this but let me double check before you post anything

Answer 4

What are your thoughts on this @MiraAngel?

Answer 5

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
What are your thoughts on this @MiraAngel?
\(\color{#0cbb34}{\text{End of Quote}}\)
This all looks like it would be correct. But if it is negative 70 it does go to the left? Don't get me wrong, that totally makes sense and that's what I would put too. I just think I that I saw somewhere that if it's a negative it goes to the right. I can check rq. But other than that it all looks great! I really appreciate ur help!

Answer 6

np, so we have \[\theta-70\] inside the parenthesis right?
For example when we have the graph of 2(x) and 2(x-3), remember that in the parenthesis everything is reversed, For example the graph of 2(x-3) is the graph of 2(x) but 3 units to the right not the left even though we are subtracting
Now back to \[\theta-70\] when we substitute an angle measure for \[\theta\] we subtract that value by 70,


Does this make any sense?

Answer 7

\(\color{#0cbb34}{\text{Originally Posted by}}\) @darkknight
np, so we have \[\theta-70\] inside the parenthesis right?
For example when we have the graph of 2(x) and 2(x-3), remember that in the parenthesis everything is reversed, For example the graph of 2(x-3) is the graph of 2(x) but 3 units to the right not the left even though we are subtracting
Now back to \[\theta-70\] when we substitute an angle measure for \[\theta\] we subtract that value by 70,


Does this make any sense?
\(\color{#0cbb34}{\text{End of Quote}}\)
Yes! It makes a lot of sense. Thank you so much. That helps a lot. :)

Answer 8

np,

Answer 9

Here's a visual of why going from f(x) to f(x-3) shifts the curve three units to the right

Let's say this is our function curve

Replacing every x with (x-3) will shift the xy axis three units to the left. This is because any given input is three less than what it used to be. Eg: x = 5 is now x-3 = 2.

Answer 10

So this is what happens after we shift the xy axis three units to the left. Keep the function curve fixed in place.

Notice how we get the illusion of the curve shifting 3 units to the right if we were to hold the xy axis in place and rather let the function move instead

Answer 11

Sorry I should relabel the new function

Answer 12

Ah, thanks for the visual way of explaining it @jimthompson5910
Good Job!

Answer 13

Thanks I appreciate the compliments. Your explanation is really good as well.