3 years ago

Graph a right triangle with the two points forming the hypotenuse. Using the sides,

Mathematics

1 answer:

valentinak56 [21]3 years ago

5 0

Answer:

Step-by-step explanation:

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Given the function f(x) = x3 + x2 − 2x + 1, what is the resulting function when f(x) is shifted to the left 1 unit?

irga5000 [103]

For this case we have the following function:

$f (x) = x ^ 3 + x ^ 2 - 2x + 1$

We apply the following function transformation:

Horizontal translations:

Suppose that h> 0

To graph y = f (x + h), move the graph of h units to the left.

We have then for h = 1:

$f (x + 1) = (x + 1) ^ 3 + (x + 1) ^ 2 - 2 (x + 1) + 1$

Rewriting we have:

$f (x + 1) = (x ^ 3 + 3x ^ 2 + 3x + 1) + (x ^ 2 + 2x + 1) + (-2x - 2) + 1$

Rewriting we have:

$f (x + 1) = x ^ 3 + 4x ^ 2 + 3x + 1$

Answer:

The resulting function when f (x) is shifted to the left 1 unit is:

$f (x + 1) = x ^ 3 + 4x ^ 2 + 3x + 1$

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