Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.

Answer 1

Each representation is matched with its respective average rate of change as follows:

1. h(x)  ⇒   4
2. f(x)   ⇒   5
3. g(x)  ⇒   2
4. j(x)  ⇒   -6

What is a rate of change?

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.

How to calculate the rate of change?

Mathematically, the rate of change for a function can be calculated by using this expression;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

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:

1. h(x)  ⇒   4
2. f(x)   ⇒   5
3. g(x)  ⇒   2
4. j(x)  ⇒   -6

Read more on rate of change here: brainly.com/question/9645290

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