Question

What is a possible solution to the graph attached inside?

**answer choices attached inside as well :)

not sure if i'm right though :/

Answer 1

graph!

Answer 2

answer choices A,B,C,D,E from top to bottom :)

I've narrowed it down to A and B... but i'm thinking that it's B since the parabola open upwards? not sure though... what do y'all think? :)

Answer 3

The easiest way to solve this problem is to look and see where the function crosses the x-axis.

Where are the 3 places where this happens?

Answer 4

crosses at x=-4, 3 and 5...

so then it would make it (x+4)(x-3)(x-5) when set to 0 right?

Answer 5

yes

Answer 6

okay :)

so how do you figure out if it's -k or k?

not sure if my reasoning is correct haha :P

Answer 7

https://www.google.com/search?q=x%5E3%2C+-x%5E3&oq=x%5E3%2C+-x%5E3&aqs=chrome..69i57.4365j0j7&sourceid=chrome&espv=210&es_sm=93&ie=UTF-8

This might help you decide.

Answer 8

Now if x gets large, what happens to the function?

Answer 9

Start from the left most point on the graph. Then travel along the curve until you hit the right most point.

From the beginning point to the end point, have you gone up or gone down?

Answer 10

ohh so would it be negative? since it keeps moving downward?

and @ybarrap when x gets larger, the function decreases?

Answer 11

@jim_thompson5910 down?

Answer 12

yep, so the the leading coefficient must be negative

Answer 13

ohh okay :) so it becomes

g(x)= -k (x+4)(x-3)(x-5) ? :)

Answer 14

The behavior for large x is determined by the highest power coefficients. So, we see that at some point x will be multiplied 3 times, giving us something times x^3. Now since we know that the function will go negative with positive x, we know something about the sign of k.

Answer 15

okay, awesome :) hehe thanks you guys!! :)

Answer 16

That's right. You did well. Thank YOU for working this out.

Answer 17

hahaa thanks @ybarrap :)

Answer 18

hahaa thanks @ybarrap :)