Given the function. calculate the following values:

f (-1) = -3

f (0) = 10

f (2) = 26

Explanation:

The given function is a piece-wise function. This means that we choose the equation to substitute in based on the given value of x (the input)

We are given that:

If the value of x is less that 0, then the function is:

f(x) = 8x + 5

If the value of x is equal to or more than 0, then the function is:

f(x) = 8x + 10

Now, let's check the required values:

a. f(-1): The given value of x is less than 0, so we substitute in the first equation

   f(-1) = 8x + 5 = 8(-1) + 5 = -3

b. f(0): The value of x is equal to 0, so we substitute in the second equation

   f(0) = 8x + 10 = 8(0) + 10 = 10

c. f(2): The value of x is more than 0, so we substitute in the second equation

   f(2) = 8x + 10 = 8(2) + 10 = 26

Hope this helps :)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!