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3 years ago

what is the rate of change of the linear function that has a graph that passes through the points (2,9) and (-1,3)?

Mathematics

1 answer:

Liono4ka [1.6K]3 years ago

4 0

Answer:

Step-by-step explanation:

slope is 2 which is the rate of change

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Fundamental theorem of calculus<br> <img src="https://tex.z-dn.net/?f=g%28s%29%3D%5Cint%5Climits%5Es_6%20%7B%28t-t%5E4%29%5E6%7D

mr_godi [17]

Answer:

$\displaystyle g'(s) = (s-s^4)^6$

Step-by-step explanation:

The Fundamental Theorem of Calculus states that:
$\displaystyle \frac{d}{dx}\left[ \int_a^x f(t)\, dt \right] = f(x)$

Where <em>a</em> is some constant.

We can let:
$\displaystyle g(t) = (t-t^4)^6$

By substitution:

$\displaystyle g(s) = \int_6^s g(t)\, dt$

Taking the derivative of both sides results in:
$\displaystyle g'(s) = \frac{d}{ds}\left[ \int_6^s g(t)\, dt\right]$

Hence, by the Fundamental Theorem:

$\displaystyle \begin{aligned} g'(s) & = g(s) \\ \\ & = (s-s^4)^6\end{aligned}$

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There are 7 7/8 cups of skittles in a Jar. If 2 1/4 cups are used for a party, how many skittes are left in the jar?

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3 years ago

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3 years ago

What is the effect on the graph of the function f(x) = 5xl when f(x) is changed to f(x – 5)?

Mekhanik [1.2K]

A change to the inside of the function notation is always a left/right or horizontal change to the graph.

Answer: A

Subtracting 5 actually shifts the graph to the right by 5 units. It's counter-intuitive and there are many ways to explain why it's the opposite of what you think it'd do, but it is a shift to the right by 5 units.

A change outside the f(x) notation is an up/down or vertical change to the graph.

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2 years ago

what is the rate of change of the linear function that has a graph that passes through the points (2,9) and (-1,3)?​

what is the rate of change of the linear function that has a graph that passes through the points (2,9) and (-1,3)?