Answer:
..
Step-by-step explanation:
..
Given the table
C : 1, 2, 3, 4, 5
F(C) : 4, 6, 8, 10, 12
Usually, the independent variable is represented by the x-value while the dependent variable (or the function) is represented by the y-value.
Thus the points represented by the table are:
(1, 4), (2, 6), (3, 8), (4, 10) and (5, 15).
The relative frequency of drawing a 4 is 25%.
A relative frequency gives us the fraction of times an event occurs.
Kenneth drew the 4 card 4 times out of 16 draws; this gives us 4/16 = 1/4 = 25%.
Answer: C) Sometimes positive; sometimes negative
============================================================
Explanation:
Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5
Plug this into f(x)
f(x) = x(x+3)(x+1)(x-4)
f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)
f(-0.5) = -0.5(2.5)(0.5)(-4.5)
f(-0.5) = 2.8125
We get a positive value.
This shows that f(x) is positive on the region of -1 < x < 0
----------------
Now pick a value between x = 0 and x = 4. I'll use x = 1
f(x) = x(x+3)(x+1)(x-4)
f(1) = 1(1+3)(1+1)(1-4)
f(1) = 1(4)(2)(-3)
f(1) = -24
Therefore, f(x) is negative on the interval 0 < x < 4
----------------
In short, f(x) is both positive and negative on the interval -1 < x < 4
It's positive when -1 < x < 0
And it's negative when 0 < x < 4