Mathematics, 12.11.2019 22:31, paigehixson342

Without using technology, describe the end behavior of f(x) = -3x4 + 7x2 - 12x + 13.

down on the left down on the right

down on the left, up on the right

up on the left, down on the right

up on the left, up on the right

Answers: 1

Show answers

Answers

answered: shawn20034

Option 1 - Down on the left down on the right

Step-by-step explanation:

Given : Function $f(x)=-3x^{4}+7x^{2}-12x+13$

To find : Without using technology, describe the end behavior of f(x) ?

Solution :

Without technology we apply characteristics of Power and Polynomial Functions

As in function $f(x)=-3x^{4}+7x^{2}-12x+13$

The the end behavior of power functions of the form f(x)=ax^n where n is a non-negative integer depending on the power and the constant.

The leading term, $f(x)=-3x^{4}$

Negative constant and even power.

So, At $x\rightarrow \infty$

$f(x)\rightarrow -\infty$

At $x\rightarrow -\infty$

$f(x)\rightarrow -\infty$

i.e. the curve approaches down on the left and down on the right.

Therefore, option 1 is correct.

answered: Guest

false

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answered: Guest

x= 1

step-by-step explanation: convert 5\frac{11}{12}5

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{5\times 12+11}{12}3.25+0.5x+1

5×12+11

2 simplify 5\times 125×12 to 6060

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{60+11}{12}3.25+0.5x+1

60+11

3 simplify 60+1160+11 to 7171

3.25+0.5x+1\frac{1}{3}+\frac{5}{6}x=\frac{71}{12}3.25+0.5x+1

4 simplify \frac{5}{6}x

x to \frac{5x}{6}

3.25+0.5x+1\frac{1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+1

5 convert 1\frac{1}{3}1

to improper fraction. use this rule: a \frac{b}{c}=\frac{ac+b}{c}a

ac+b

3.25+0.5x+\frac{1\times 3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

1×3+1

6 simplify 1\times 31×3 to 33

3.25+0.5x+\frac{3+1}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

3+1

7 simplify 3+13+1 to 44

3.25+0.5x+\frac{4}{3}+\frac{5x}{6}=\frac{71}{12}3.25+0.5x+

8 simplify 3.25+0.5x+\frac{4}{3}+\frac{5x}{6}3.25+0.5x+

to \frac{13.75}{3}+\frac{4x}{3}

13.75

\frac{13.75}{3}+\frac{4x}{3}=\frac{71}{12}

13.75

9 simplify \frac{13.75}{3}

13.75

to 4.5833334.583333

4.583333+\frac{4x}{3}=\frac{71}{12}4.583333+

10 subtract 4.5833334.583333 from both sides

\frac{4x}{3}=\frac{71}{12}-4.583333

−4.583333

11 simplify \frac{71}{12}-4.583333

−4.583333 to \frac{4}{3}

\frac{4x}{3}=\frac{4}{3}

12 multiply both sides by 33

4x=\frac{4}{3}\times 34x=

×3

13 simplify \frac{4}{3}\times 3

×3 to \frac{12}{3}

4x=\frac{12}{3}4x=

14 simplify \frac{12}{3}

to 44

4x=44x=4

15 divide both sides by 44

x=1

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Without using technology, describe the end behavior of f(x) = -3x4 + 7x2 - 12x + 13.

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