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.
3. The function f(x) passes through the points (−4, 6) and (−2, 3)
The function g(x) is represented by the equation g(x)=1/2x^2−3 .
Which of the following statements is true of these two functions?
A. On the interval [−4,−2] the average rate of change for f(x) is equal to −2 which means that f(x) is changing at a faster rate than g(x)
B. On the interval [−4,−2] the average rate of change for f(x) is equal to −3/2 which means that f(x) is changing at a faster rate than g(x)
C. On the interval [−4,−2] the average rate of change for g(x) is equal to 3 which means that g(x) is changing at a faster rate than f(x) .
D. On the interval [−4,−2] the average rate of change for g(x) is equal to −3 which means that g(x) is changing at a faster rate than f(x)
1. B. g(x) has the greater relative maximum value of 4.
2. B. No, the relative maximum of f(x) is -3, and the relative maximum of g(x) is -4.
3. D. On the interval [−4,−2] the average rate of change for g(x) is equal to −3 which means that g(x) is changing at a faster rate than f(x).