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Each representation is matched with its respective average rate of change as follows:
- h(x) ⇒ 4
- f(x) ⇒ 5
- g(x) ⇒ 2
- j(x) ⇒ -6
A rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.
<h3>How to calculate the rate of change?</h3>Mathematically, the rate of change for a function can be calculated by using this expression;
Thus, the average rate of change over the given interval [a, b] is given by:
r = [f(b) - f(a)]/(b - a)
Where:
The interval is [0, 2], so a = 0 and b = 2
Substituting the given parameters into the formula, we have;
r = [f(2) - f(0)]/(2 - 0)
r = [f(2) - f(0)]/2
For the first function h(x), we have:
r = [h(2) - h(0)]/2
When x = 2
h(2) = 2² + 2(2) - 6
h(2) = 4 + 4 - 6
h(2) = 2.
When x = 0
h(0) = 0² + 2(0) - 6
h(0) = 0 + 0 - 6
h(0) = -6.
Evaluating the function, we have:
r = [h(2) - h(0)]/2
r = [2 - (-6)]/2
r = (2 + 6)/2
r = 8/2
r = 4.
For the second function f(x), we have:
Note: The x-intercept is at (2, 0), so x = 2 and f(2) = 0 while its y-intercept at (0, -10), so x = 0, f(0) = -10
r = [f(2) - f(0)]/2
r = [0 - (-10)]/2
r = (0 + 10)/2
r = (10)/2
r = 5.
For the third function g(x), we have:
Note: g(2) = 6 and g(0) = 2 on the graph.
r = [g(2) - g(0)]/2
r = (6 - 2)/2
r = 4/2
r = 2.
For the fourth function j(x), we have:
Note: From the table, x = 2 outputs j(2) = -8 while x = 0 outputs j(0) = 4.
r=[j(2) - j(0)]/2
r = (-8 - 4)/2
r = -12/2
r = -6.
In conclusion, we can infer and logically deduce that each representation is matched with its respective average rate of change as follows:
- h(x) ⇒ 4
- f(x) ⇒ 5
- g(x) ⇒ 2
- j(x) ⇒ -6
Read more on rate of change here: brainly.com/question/9645290
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