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3 years ago

which of the following correctly describes the end behavior of the polynomial function, f(x)=2x^4-3x^2+2x

Mathematics

2 answers:

Gnom [1K]3 years ago

8 0

Answer:

The end-behavior of the given function is: "Both ends upward".

Step-by-step explanation:

Given polynomial function is: $f(x)=2x^4-3x^2+2x$

For determining the end-behavior of a polynomial function, first we need to identify the degree and leading coefficient.

Degree means the highest exponent to the variable in the function. So, here degree is 4.

Leading coefficient is the coefficient of the first term in the function. So, here the leading coefficient is 2.

Now the rule is: If the degree of the polynomial function is even and the leading coefficient is positive, then both ends of the graph of function will be in upward direction.

So, the end-behavior of the given function is: "Both ends upward".

inna [77]3 years ago

4 0

Answer:

Both ends go up.

Step-by-step explanation:

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3 years ago

Factor 7x3y4−7x2y5 completely.

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Answer:

Step-by-step explanation:

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3 years ago

How is the series 5+11+17…+251 represented in summation notation?

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Answer:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

Step-by-step explanation:

Given:

Series 5+11+17+...+251

To find:

Summation notation of the given series

Summation Notation:

$\displaystyle \large{\sum_{k=1}^n a_k}$

Where n is the number of terms and $\displaystyle \large{a_k}$ is general term.

First, determine what kind of series it is, there are two main series that everyone should know:

Arithmetic Series

A series that has common difference.

Geometric Series

A series that has common ratio.

If you notice and keep subtracting the next term with previous term:

11-5 = 6
17-11 = 6

Two common difference, we can in fact say that the series is arithmetic one. Since we know the type of series, we have to find the number of terms.

Now that brings us to arithmetic sequence, we know that first term is 5 and last term is 251, we’ll be finding both general term and number of term using arithmetic sequence:

Arithmetic Sequence

$\displaystyle \large{a_n=a_1+(n-1)d}$

Where $\displaystyle \large{a_n}$ is the nth term, $\displaystyle \large{a_1}$ is the first term and $\displaystyle \large{d}$ is the common difference:

So for our general term:

$\displaystyle \large{a_n=5+(n-1)6}\\\displaystyle \large{a_n=5+6n-6}\\\displaystyle \large{a_n=6n-1}$

And for number of terms, substitute $\displaystyle \large{a_n}$ = 251 and solve for n:

$\displaystyle \large{251=6n-1}\\\displaystyle \large{252=6n}\\\displaystyle \large{n=42}$

Now we can convert the series to summation notation as given the formula above, substitute as we get:

$\displaystyle \large{\sum_{n=1}^{42}(6n-1)$

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2 years ago

Which of the lists is in order from smallest to largest? 1,330; 3,130; 3,310; 3,031 3,130; 3,031; 3,310; 1,330 1,330; 3,310; 3,0

lesantik [10]

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3 years ago

Read 2 more answers