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3 years ago

How does the graph of the function g(x) = 5x + 1 differ from the graph of f(x) = 5*?

Mathematics

1 answer:

elena-14-01-66 [18.8K]3 years ago

7 0

Answer:

C. It is translated up 1 unit.

Step-by-step explanation:

Translations of a function f(x)

To translate a function f(x) a units to the right, we have f(x-a)

To translate a function f(x) a units to the left, we have f(x+a)

To translate a function f(x) a units up, we have f(x) + a

To translate a function f(x) a units down, we have f(x) - a

In this question:

g(x) = 5x + 1

f(x) = 5x

This means that the function g(x) is 1 added to the function f(x), that is, it is translated up 1 units, and the correct answer is given by option c.

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Match the base and height to the volume of the prism.<br><br> B = 6 square units<br> h = 12 units

Finger [1]

We have a prism with a volume of 16y⁴ + 16y³ + 48y² cubic units.

Its volume is equal to the area of its base times its height.

Of course, for those to be the base area and height of this prism, they would have to multiply to 16y⁴ + 16y³ + 48y² cubic units.

Let's test each of these answers to see which gives us the correct volume.

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a base area of 4y square units and height of 4y² + 4y + 12 units

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Distribute the 4y to each term inside the parentheses.

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This is not the right volume, so these can not be dimensions of our prism.

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a base area of 8y² square units and height of y² + 2y + 4 units

We find the volume by multiplying the base area by the height...

8y²(y² + 2y + 4)

Distribute the 8y² to each term inside the parentheses.

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a base area of 12y square units and height of 4y² + 4y + 36 units

We find the volume by multiplying the base area by the height...

12y(4y² + 4y + 36)

Distribute the 12y to each term inside the parentheses.

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This is not the right volume, so these can not be dimensions of our prism.

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a base area of 16y² square units and height of y² + y + 3 units

We find the volume by multiplying the base area by the height...

16y²(y² + y + 3)

Distribute the 16y² to each term inside the parentheses.

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The volume fits, so these could be the base area and height of our prism.

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D. a base area of 16y² square units and height of y² + y + 3 units

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Answer:

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Step-by-step explanation:

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1+10.584= 11.584

11.584 squared

=134.189

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