Average rate of change of polynomials
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Problem
g(t)= -(t-1)^2 +5g(t)=−(t−1)
2
+5g, left parenthesis, t, right parenthesis, equals, minus, left parenthesis, t, minus, 1, right parenthesis, squared, plus, 5
What is the average rate of change of ggg over the interval -4\leq t\leq 5−4≤t≤5minus, 4, is less than or equal to, t, is less than or equal to, 5?

1

Step-by-step explanation:

g(t)= -(t -1 )² +5

1. Calculate the values of g(-4) and g(5)

g(-4) = -(-4 - 1)² + 5 =  -(-5)² + 5 = -25 + 5 = -20

g(5) = -( 5 - 1)² + 5 =  - (4)² + 5 =  -16 + 5 =  -11

2. Calculate the average rate of change

Rate of change = (y₂ - y₁)/(x₂-x₁) = [-11 -(-20)]/[5 - (-4)] = (-11+ 20)/(5 + 4) = 9/9 = 1

The average rate of change is 1.

In the figure below, the red curve represents the function g(t), while the black dashed line represents the average rate of change over the interval [-4,5].

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

answer:   c ?

step-by-step explanation: