Which of the following is an odd function?

f(x) = -x is odd

Step-by-step explanation:

A function f is odd if f(-x) = -f(x) for all x in the domain of f. Then, let's check each of the functions.

1. f(x) = x^3 + 5x^2 + x

f(-x) = (-x)^3 + 5(-x)^2 + (-x) = -x^3 + 5x^2 - x

-f(x) = -(x^3 + 5x^2 + x) = -x^3 - 5x^2 - x

Given that f(-x) ≠ -f(x). The function f is not odd.

2. f(x) = sqrt(x)

f(-x) = sqrt(-x) (Imaginary number)

-f(x) = -sqrt(x)

Given that f(-x) ≠ -f(x). The function f is not odd.

3. f(x) = x^2 + x

f(-x) = (-x)^2 -x = x^2 - x

-f(x) = -x^2 - x

Given that f(-x) ≠ -f(x). The function f is not odd.

4. f(x) = -x

f(-x) = - (-x) = x

-f(x) = -(-x) = x

Given that f(-x) = -f(x). The function f is odd.

The equation is y = $72.99 + $28.45(x - 1), where y is the monthly charge and x is the month in which it is calculated.

Step-by-step explanation:

Step 1; First we need to establish a relation between the difference in costs. For the first month it cost $72.99, during the second month, it costs $101.44 and in the third month, it costs $129.89. Difference in rates

Second months rate - First months rate = $101.44 - $72.99 = $28.45

Third months rate - Second months rate = $129.89 - $101.44 = $28.45.

So for every consecutive month, the charges increase by $28.45

Step 2; Now we develop an equation,

y = $72.99 + $28.45(x - 1), where y is the charge that month and x is the month in which it is calculated.

For x = 1, y = $72.99 + $28.45(1 - 1) = $72.99 + $28.45(0) = $72.99,

For x = 2, y = $72.99 + $28.45(x - 1) = $72.99 + $28.45(2 - 1) = $101.44,

For x = 3, y = $72.99 + $28.45(3 - 1) = $72.99 + $28.45(3-1) = $129.89.

So this is the equation to calculate the cost y the mobile provider charges in month x.