1. The function f(x) is quadratic, it opens down and has a vertex at (−2, 3) . The function g(x) has the following table of values:
X -4 -3 -2 -1 0
g(x) 1 4 2 -2 -5
Which function has a greater relative maximum value on the interval x=−4 to x=−1 , an what is the value of that greater relative maximum?
A. f(x) has the greater relative maximum value of -2.
B. g(x) has the greater relative maximum value of 4.
C. f(x) has the greater relative maximum value of 3.
D. g(x) has the greater relative maximum value of -3.
2. Question An absolute value function, f(x) , is represented by the table of values.
X -4 -3 -2 -1 0
f(x) -9 -7 -5 -3-5
The function g(x)=−2|x+1|−2
Does f(x) have the lesser relative maximum value than g(x) on the interval [−4, 0] ?
A. Yes, the relative maximum of f(x) is -3, and the relative maximum of g(x) is -2.
B. No, the relative maximum of f(x) is -3, and the relative maximum of g(x) is -4.
C. Yes, the relative maximum of f(x) is -5, and the relative maximum of g(x) is -2.
D. Yes, the relative maximum of f(x) is -5, and the relative maximum of g(x) is -4.
1. To compare the relative maximum values of f(x) and g(x) on the interval x = -4 to x = -1, we need to determine the vertex of g(x). The vertex of a quadratic function in the form g(x) = ax^2 + bx + c can be found using the formula x = -b / (2a).
For g(x), we can see that the table of values has the highest point at x = -3 with a value of 4. This suggests that the vertex is located at (-3, 4).
Therefore, the correct statement is: B. g(x) has the greater relative maximum value of 4.
2. Comparing the relative maximum values of f(x) and g(x) on the interval [-4, 0]:
For f(x), we can see from the table of values that the highest point occurs at x = -1 with a value of -3.
For g(x) = -2|x+1| - 2, the absolute value function |x+1| is always non-negative, so the highest point of g(x) occurs when |x+1| is equal to 0. This happens at x = -1. Plugging this value into g(x), we get g(-1) = -2(0) - 2 = -2.
Therefore, the correct statement is: A. Yes, the relative maximum of f(x) is -3, and the relative maximum of g(x) is -2.