hi! the assignment is two different part so i will upload them under files. part 1 has 2 pages which means 2  photos and part 2 has 1 page. i marked on every photo so you dont get confused. remenber to give all deteiled solution to each problem and solution must be hand writing please. zoom photos for better reading and let me know if you have any question. thanks

tips : you can help yourself with these exemples :

Even and odd functions Examples

Identifying even and odd functions

A function f is an even function if

f (-x) = f (x) for all x in the domain of f

The graph of an even function is symmetric to the y-axis

A function f is an odd function if

f (-x) = – f (x) for all x in the domain of f

The graph of an even function is symmetric to the origin Note. (- x)even = xeven

(-x)odd = -xodd

|-x| = |x|

Procedure to determine even, odd, or neither function

Given a function f(x). Determine if thew function is even, odd, or neither

Step 1. Find f(-x)

Step 2. Check f(-x) = f(x)? If so then f(x) is even function. If not, go to Step 3

Step 3. Find -f(x). Check f(-x) = -f(x)? If so then f(x) is odd function. if not, go to Step 4 Step 4. Write the answer: f(x) is neither even nor odd —————————————————————————————————————- Example 1. f(x) = 2×6 3×2 + 4|x| -2

f(x)=2×6 3×2 +4|x|-2

1.f(-x)=2(-x)6 3(-x)2 +4|-x|-2=2×6 3×2 +4|x|-2

2. As you see f(x) = f(-x) therefor f(x) = 2×6 3×2 + 4|x| -2 is an even function Example 2. f(x) = -3×7 + 5×3 + 3x

f(x)=-3×7 +5×3 +3x

1. f(-x) = -3(-x)7 + 5(-x)3 + 3(-x) = 3×7 -5×3 3x, so

2. f(x) f(-x)

3.-f(x)=-(-3×7 +5×3 +3x)=3×7 -5×3 3x

     

4. f(-x) = -f(x), therefor

5. f(x) = -3×7 + 5×3 + 3x is an odd function Example3.f(x)=3×5 +4×3 x

1.f(-x)==3(-x)5 +4(-x)3 (-x)=-3×5 -4×3 +x,so

2. f(x) f(-x) therefore it is not an even function 3.-f(x)=-(3×5 +4×3 x)=-3×5 -4×3 +x

4. f(-x) -f(x) therefore it is not an odd function

5. f(x) = 3×5 + 4×3 x is neither even nor odd function