Question

Given the function f(x) = −3x^3 + 9x^2 − 2x + 3, what part of the function indicates that the left end starts at the top of the graph?

The degree of the first term. Can't be this, already did that, was incorrect.
The degree of the last term
The coefficient of the first term. I think its this.
The coefficient of the last term

Answer 1

What a strange question. It is BOTH the degree AND the coefficient on that first term.

Since it has nothing to do with the constant term, your choices are limited.

Answer 2

Don't really know how to answer this.

Graphing points are (-1,17), (0,3), (1,7), (2,11), and (3,-3)

Answer 3

Looks fine. A little jerky, but that's the fault of the drawing tools.

Answer 4

Crude drawing, wish there was someplace I could draw something more precise. Calculator called mathway has graphing but I can't link it to you.

Answer 5

It's fine the way it is. Label that zero.

Answer 6

The X intercept is just behind 3x.

Answer 7

But, still not too sure about how to answer this. Lesson for it gave jack on how to.

Answer 8

Sure, somewhere between x=2 an x=3.

How's your synthetic division?

Answer 9

Know synthetic division decently.

Answer 10

That's one day to narrow down the zero.

"Bisection" suggests you try x = 2.5 net.

Alternatively, linear interpolation often gives a good first guess.

(2,11), (3,-3) ==> 2 + 11/14 = 2.7857142857142857 (so, 2.8?)

Answer 11

Ran through that and into my calculator, super specifics say x=2.889053

Answer 12

Otherwise rounded to 2.89.

Answer 13

x intercept = (2.89, 0)
y intercept = (0,3)

Answer 14

Would it be the coefficient of the first term?

I do know it cannot be the degree.

Answer 15

Original question, has been the same.

Running the problem best to my knowledge it would have to be coefficient of the first

Answer 16

See, my linear approximation wasn't bad.

As far as "first" or "last", we would have to determine which way were counting. In any case, it's the term with the greatest degree.

Answer 17

Well the greatest degree is 3x^3.

Answer 18

Yes, Yes it is. Since the degree is 3(odd), we have

Positive coefficient ==> comes in from the bottom
Negative coefficient ==> comes in from the top

Answer 19

Copy, so coefficient of the first term?

Answer 20

Nope, coefficient AND degree.

If the degree is 4(even), we have

Positive coefficient ==> comes in from the top
Negative coefficient ==> comes in from the bottom

Answer 21

So last term?

Answer 22

@tkhunny

Answer 23

"first" and "last" are not meaningful unless you state "standard form" or something else that specifies the order. Stick with "term of highest degree" and it will require no other explanation.

Answer 24

But −3x^3 + 9x^2 − 2x + 3 written in standard form is the same isn't it?

Answer 25

Which is the "first" term and which is the "last"? It depends on which way you count?

Answer 26

First term would be 3x^3 correct?

Answer 27

Asked and answered, Highest Degree.