Question

What is the end behavior of the graph? (Please help!)

Answer 1

4th option:
As `x->oo, f(x)->-oo`
As `x->-oo, f(x)->-oo`

Explanation:

Look at what the graph here is doing.

As x is getting bigger, after the turning point, we see that `f(x)` is getting smaller and smaller; its getting lower and lower on the y-axis. This means that as x gets larger and closer and closer to infinity, `f(x)` is also going to get smaller and closer and closer to `-oo`.

Something similar is true before the turning point. Before this turning point, as x gets lower and further to the left on the x-axis, `f(x)` gets lower and lower, towards `-oo`.

so:
As `x->oo, f(x)->-oo`
As `x->-oo, f(x)->-oo`

Answer 2

As `x` approaches positive infinity `f(x)` approaches negative infinity

As `x` approaches negative infinity `f(x)` approaches negative infinity

Explanation:

This is the standard form of `y=-ax^2` where `a` is some constant.

This is the same as `(-1)xxaxx x^2`

As `ax^2` is negative the general shape is of form `nn`

As `x` grows then `-ax^2` becomes more and more negative.

For where `x>0`

`y= lim_(x-> + oo)(-ax^2) ->-oo`

For where `x<0`

`y= lim_(x-> - oo)(-ax^2) ->-oo`

as `(-1)xxaxx (-oo)^2color(white)("ddd") ->color(white)("ddd") (-1)xxaxx(+oo)`

Answer 3

`"see explanation"`

Explanation:

`"as "xto+oo,f(x)to-oodarr`

`"as "xlarr-oo,f(x)to-oodarr`

`"this would indicate the graph of a polynomial of even"`
`"degree with negative leading coefficient"`

`"the answer is the last one on the grid shown above"`
`"in the question"`