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aalyn [17]
3 years ago
6

If f(x)=logx, explain the transformation that occurs when f(0.25(x-5))+3

Mathematics
1 answer:
nevsk [136]3 years ago
6 0

Answer:

First, let's explain the transformations in a general way:

Vertical shift.

If we have a function f(x), a vertical shift of N units is written as:

g(x) = f(x) + N

This will move the graph of f(x) up or down a distance of N units.

if N is positive, then the shift is upwards

if N is negative, then the shift is downwards.

Horizontal shift.

If we have a function f(x), a horizontal shift of N units is written as:

g(x) = f(x + N)

This will move the graph of f(x) to the right or left a distance of N units.

if N is positive, then the shift is to the left

if N is negative, then the shift is to the right.

Horizontal dilation/contraction.

For a function f(x), an horizontal contraction dilation is written as:

g(x) = f(k*x)

where:

k is called the "scale factor"

If k < 1, then the graph "dilates" horizontally.

if k > 1, then the graph "contracts" horizontally.

Now, in this problem we have:

f(x) = log(x)

And the transformed function is:

g(x) = f(0.25*(x - 5)) + 3

Then, the transformations that take place here are, in order:

Vertical shift of 3 units up:

g(x) = f(x) + 3.

Horizontal shift of 5 units to the right:

g(x) = f(x - 5) + 3

Horizontal dilation of scale factor 0.25

g(x) = f( 0.25*(x - 5)) + 3

replacing f(x) by log(x) we have

g(x) = log(0.25*(x - 5)) + 3.

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Marcus finds that (3x^2-2y^2+5x)+(4x^2+12y^2-7x)=7x^2-10y-2x. What error did Marcus make?
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Answer:

7x^2+10y^2-2x is the correct answer, Marcus put -10y INSTEAD of +10y^2

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Combine like terms- I'll add x^2 first, then y^2, and then finally x, and it will be in that order.

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Make sure to check your signs are correct, and you wrote down the proper exponents.




4 0
3 years ago
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The total cost to produce x handcrafted wagons is C(x) = 110 + 7x - x^2 + 2x^3. Find the marginal cost when x = 8.
nataly862011 [7]
<h2>Answer:</h2>

The marginal cost when x=8 is:

                          375

<h2>Step-by-step explanation:</h2>

We know that the marginal function for a cost function C(x) at x=a

is given by:

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Here we have the cost function C(x) as:

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Now we find the derivative of C(x) with respect to x.

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9x + 4 ≤ 58

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1/6x − 2 > 3

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3 years ago
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