Answer:
4 IS THE ANSWER MATE
Explanation:
Absolutely, I can do that!
Let's take a look at each statement:
1) f(x) has a y-intercept at (0,2)
To find the y-intercept, we need to set x to 0 and solve for y. Plugging in x = 0 into the equation for f(x), we get:
f(0) = -log(0+4) + 2
f(0) = -log(4) + 2
f(0) = -0.602 + 2
f(0) = 1.398
Since the y-coordinate of the y-intercept is 1.398, not 2, this statement is false.
2) The function -f(x) has a y-intercept at (0,2)
Since the negative sign in front of f(x) reflects the graph of f(x) across the x-axis, we can determine the y-intercept of -f(x) by taking the opposite of the y-intercept of f(x). Since the y-intercept of f(x) is not 2, this statement is also false.
3) As x approaches positive infinity, the function f(x) approaches negative infinity.
The function f(x) is a logarithmic function with a negative coefficient, which means it approaches negative infinity as x approaches positive infinity. Therefore, this statement is true.
4) As x approaches -4 from the right, the function f(x) approaches negative infinity.
As x approaches -4 from the right, the value of f(x) becomes more and more negative without bound, which means that f(x) approaches negative infinity as x approaches -4 from the right. Therefore, this statement is also true.
In summary, statements (1) and (2) are false, while statements (3) and (4) are true.