Assignment
1

Investigation
2

Make
up ** linear **functions

i.
**h(x) = f(x) + g(x)**

ii.
**h(x) = f(x).g(x)**

iii.
**h(x) = f(x)/g(x)**

iv.
**h(x) = f(g(x))**

Summarize
and illustrate.

So
choosing **f(x)= x ^{2}+5**

and
**g(x)=2x+17**

We
get

(i) **h(x)=f(x)+g(x)=(x ^{2}+5)+(2x+17)**

(ii.) **h(x)=f(x)****×****g(x)= (x ^{2}+5)**

** **

(iii.)** h(x)=f(x)/g(x) )= (x ^{2}+5)/(2x+17)**

(iv.)** h(x)=f(g(x)) )= ((2x+17) ^{2}+5)**

To
make this easier to see letŐs put all the graphs together

You
can see the progression into becoming a straight line. Starting from f(x) and
going to g(x) with the different operations.

Now,
letŐs choose different values of f(x) and g(x) and observe what happens.

LetŐs
take f(x)=x^{4}+5x+10

and
g(x)=sin(x)+x^{2}+3

Now
we get

(i.)
h(x)=f(x)+g(x)=(x^{4}+5x+10)+(sin(x)+x^{2}+3)

(ii.)
h(x)=f(x)×g(x) =(x^{4}+5x+10)×(sin(x)+x^{2}+3)

(iii.)
h(x)=f(x)/g(x)=(x^{4}+5x+10)/(sin(x)+x^{2}+3)

(iv.) h(x)=f(g(x))= ((sin(x)+x^{2}+3)^{4}+5x+10)

Now,
letŐs put them all on the same graph so that it is easier to make an
observation

Again,
you can notice the same general progression. Clearly these operations merely change the position of the
graph along the y-axis, but not itŐs shape until division comes into play.