Answer:
Step-by-step explanation:
f(x) is quadratic function and g(x) is linear (since AP in the right column).
Find the equation of the function f(x), use the points on the graph:
- c = 5 as the y-intercept is (0, 5)
- a(-1)² + b(-1) + 5 = 0 ⇒ a + 5 = b
- a(5²) + b(5) + 5 = 0 ⇒ 25a + 5b + 5 = 0 ⇒ 25a + 5a + 25 + 5= 0 ⇒ a = -1 ⇒ b= 4
The function is:
Find the equation of g(x)
Find the slope of g(x):
- m = (1 - 7)/(-1 + 4) = -2
Use (-4, 7) to find its equation:
- y - 7 = -2(x + 4)
- y = -2x + 7 - 8
- y = -2x - 1
See the required comparison below
The y-intercepts:
- f(x) ⇒ 5,
- g(x) ⇒ -1
- -5 < - 1
Values at x = 3:
- f(3) = -3² + 4(3) + 5 = 8
- g(3) = -2(3) - 1 = - 7
- 8 > 7
Average rate of change in the interval [2,5]:
- f(x) ⇒ (0 - 9)/(5 - 2) = -3
- g(x) ⇒ (-11 + 5)/ (5 - 2) = -2
- -3 < -2
Max of function in the interval [-5, 5];
- f(x) ⇒ 9, vertex of the function
- g(x) ⇒ g(-5) = -2(-5) - 1 = 9, taken the least point of x as it is a decreasing function
- 9 = 9
