Cobby's Methods Questions

[plato]

Hey all ive got another question


 Use a graphic calc to determine the co-ordinates of the turning points correct to two decimal places.
How do i do that?

Thanks

2nd >> Trace >> 4 (maximum)
Get the cursor on the left of the maximum turning point (left bound) which is near x = 0. ENTER
Get the cursor on the right of the maximum turning point (right bound) which is near x = 0. ENTER.
Press ENTER again.
Should get x = -0.305 and y = .486 to three decimal places (not sure how many they want)

Repeat this for the minimum turning point.

Sorry Dekoyl but you definitely should NOT use Trace to find any of the major points with any calculator whether in Methods or Methods CAS. Each calculator will have a function somewhere that finds max/min ponts, intersections, zeroes etc.

If you read the instructions carefully, he did give instructions for using functionality for finding max/min points.

Yeah - you're right. I just saw the word Trace and should have read the rest. He was referring to the button rather than the operation. Sorry dekoyl.

[cobby]

Can someone please help me with this?

{}
{}
Is there a way that i can find the range, by sketching and without sketching the graph?

Thanks

[/0]

A graph without a y-variable? 


If you want to solve algebraically you have to consider 2 cases:

, then , i.e. and if

, then , i.e.

So the values x can take are

[Flaming_Arrow]

i would start looking at the translations

Domain is R because |x| is R

Range is in |x| so this one is moved down by -5 hence

[cobby]

Sketch the graph of
My working so far is, 

and

Then



Have i done this right?? Where do i go from here to be able to sketch the graph?

[bucket]

draw and translate it up by one unit along the y axis.

[dekoyl]

Yes, draw |x-4| and translate up by one unit. It's "sharp point" should be at (4,1).
The y-intercept is found using:
-(0 - 4) = y
y-int = (0,4)

PS: I use -(x-4) = y because the graph as you are aware, consists of y=x - 4 and y=-(x-4). The y-intercept lies on the part of the graph where it's y=4-x.

[cobby]

Hey all, another question

For the line to be tangent to the circle with equation
Find the value of k

Thanks

[/0]

The discriminant must be equal to zero for one solution (and hence tangency)

[cobby]

What did you do exactly to get from

to

[Flaming_Arrow]

use the discriminant formula



where

[dekoyl]

That's the discriminant.
of that is and because we know it will have only one solution (for tangency), it will equal 0

[cobby]

Hey all, this ones a composite function question
Thanks




a) Find and state range

b) Find and state range

[Mao]

to use "\" in latex, the command is "\backslash", "{" is "\{", "}" is "\}"


First, we note that the horizontal asymptote for g(x) is at y=0 (no vertical translation), i.e. the range of g is R\{0}, which fits in the domain of f, so f(g(x)) exists for the entire domain of g.



The range is hence

use similar reasoning for b) and arrive at


It should be noted that when , f and g are inverse functions of each other.

[cobby]

Hey all im stuck on this polynomial question

Find the rule for the cubic function, the graph of which passes through the points (1,1) (2,4) (3,9) and (0,6)

Thanks