Final project for Precalc. Walk through of 4 different problems from different units that we studied.

2. Let’s start with an easier problem to do. In
this problem, I’m going to give you an
f(x) function, h(x) function, and a g(x)
function and we will walk through the
indicated operation. After that we will
find the domain and range of the final
function

3. 
First find G(F(x)) by substituting the x in
the G function for the F function
› G(F(x))= (4x²+16x)-6

Now put this in the H function and
simplify
› H(G(F(x)))= 4x²+16x-4 (-6+2= -4)
4
› H(G(F(x)))= x²+4x-1

4. 
For quadratics, domain is all real numbers!
› Domain: (-∞,∞)

With a positive a value (number in front),
the range will be K (last number) to infinity
› Range: [-1, ∞)
 Remember to include the -1 so use a bracket
around the number

Just like that we are done with the first
problem.

5. In this problem I am going to give an
equation in standard form. From there
we will convert to factored form and
vertex form. That is not all folks. We are
going to find the vertex, x-intercepts and
y-intercepts as well. Finally we will graph
it all. Let’s get cracking.

6. 
Simply factor this into 2 parentheses like
normal to get factored form
› F(x)= (x+8)(x-4) ← factored form

To find x- intercepts use factored form
› Remember intercepts are when the parentheses
equal 0
 X=-8 x=4 ← x-intercepts

To find y-intercepts use standard form
› Use the c value (last number) to find intercept
 (0, -32) ← y-intercept

7. 
To find vertex form we need to complete
the square using standard form

To find the vertex, use vertex form for
obvious reasons
› Use the opposite of the number in parentheses
(make equal to 0) and number on outside
 (-2, -36) ← vertex

8. 
Plot all points before you make graph

9. Before we start this, it’s okay if you take a
quick breather. Math can be a lot to
handle sometimes. I’m not judging.
Let’s move on to learn a bit about
rationals. I’m going to give a function
and together we will find x and yintercepts, holes, vertical and horizontal
asymptotes. Not too shabby if I do say so
myself.

10. Factor both the numerator and
denominator. Make sure to look for
greatest common factor.
 The factored function should look like

› (x+7)(x-3)
x+7 can be divided out (hole!)
3(x+7)(x-4)

The function is now
› (x-3)
3(x-4)
with a hole at x= -7 (makes it 0!)

11. 
To find x- intercepts look to the
numerator in factored form. We need to
find the number that will make the
numerator 0.
› In this case the x-int. is (3,0)

To find the y- intercept we look at
standard form. We plug 0 in for x and see
what is left over which in this case is -21/84.
› After simplifying the y-intercept is (0, ¼)

12. 
To find the horizontal asymptote, we
divide the leading coefficients. I’ve
made it easier by having the highest
power in the num. and den. the same.
› The H.A. is where y= 1/3

To find the vertical asymptote, we look
where the denominator will equal 0 using
factored form.
› The V.A. is where x = -4

14. We are almost done figuring out problems
together. Let’s cruise through this last
problem and consider ourselves
accomplished people. This last one is
meant to be a challenge so don’t get
flustered, we will get through it. I’m going
to give a function and we will find xintercepts, graph and find domain. Let’s
do this.

15. 
I gave a solution so we will use it to long
divide
› Remember to use the rule: divide, distribute
subtract, drop.

Set it up like this: (leave space on top)

17. 
We have one solution (x= -5) and x³=4x²9x-36. Luckily this one groups! Here is how
to do it.

18. Our 4 solutions: x=3, x= -3, x= -4, x= -5
 We have a positive a value and an even
degree (number of solutions) so graph
will look like a w.


Domain has to be where y is positive
› Domain: (-∞, -5]U[-4, -3]U[3,∞] (include
intercepts with brackets)
↑ means union

19. Thanks for looking through my D.E.V.
project. I hope that it was at least a little
bit helpful for you. This project may have
been hard but it was worth it.
“Tell me and I forget. Teach me and I remember. Involve
me and I learn.”
-Benjamin Franklin
Swag

20. http://prezi.com/33gbxyl
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