Assignment on Algebra PDF

ALGEBRA
STUDENT NAME/ID
[Pick the date]

Question 1
Given piecewise function
f(x)={
(a) f(0)=?
Here,
3
2 x+3forx≤0 wouldbetakenintoaccount
Now,
f(0)=(3
2 )∗0+3=3
(b)f(2)=?
Here,
(x−1)2+2for0<x≤2wouldbetakenintoaccount
Now,
f(2)=(2−1)2+2=3
Question 2
The correct graph would be Graph A. This is because f(x+1) would involve shifting of the
whole graph of f(x) one unit to the right and -1 would imply a downward vertical shift for every
value of the graph. Both these attributes are captured in graph A.
Question 3
f(x)=3 x2−x3
1

A function would be even when f(−x)=f(x)forallx∈R
A function would be odd when f(−x)=−f(x)forallx∈R
Now,
f(x)=3 x2−x3
f(−x)=3(−x)2−(−x)3
f(−x)=3x2+x3
It can be seen from the above that f(−x)≠f(x)and hence, function is not even function.
Further, f(−x)≠−f(x)and hence, function is not odd function.
Therefore, it can be concluded that given function f(x)=3 x2−x3is neither an even nor an odd
function.
Question 4
a) x axis – NO, y axis- No, Origin – Yes
b) x axis – NO, y axis- Yes, Origin – NO
Question 5
a) The given function is increasing on (-∞,0] U [3.5]
b) Domain: (--∞,,5] Range: (--∞,,4]
Question 6
Let
2