deteermine algebracially whether the given function is even,odd, or neither.
f(x)= -3x-/9/
neither.
x is odd
9 is even
Given the function f(x) = x^3+ 3x
a. Find the rate of change between the two stated values for x: 1 to 2
b. Find the equation of a secant line containing the given points: (1, f(1)) and (2, f(2))
To determine whether a function is even, odd, or neither, we need to examine its algebraic properties.
1. Even functions: If a function f(x) satisfies f(-x) = f(x) for all values of x in its domain, then it is an even function. In other words, when you replace x with its opposite, the function remains the same.
2. Odd functions: If a function f(x) satisfies f(-x) = -f(x) for all values of x in its domain, then it is an odd function. In other words, when you replace x with its opposite, the function changes sign.
Let's apply these definitions to the given function f(x) = -3x - |9|:
First, let's evaluate the function at -x:
f(-x) = -3(-x) - |9|
= 3x - 9
Now, let's evaluate the function at x:
f(x) = -3x - |9|
Since f(-x) ≠ f(x) and f(-x) ≠ -f(x), we can conclude that the given function f(x) = -3x - |9| is neither even nor odd.
Therefore, the function is neither even nor odd.