Answer:
Domain is all real numbers.
The range is
The function is increasing over .
The function is decreasing over
The function has a positive y-intercept.
-----------------This is a guess if I had interpreted your choices correctly:
Second option: The range is
Third option: The function is increasing over .
Last option: The function has a positive y-intercept.
I can't really read some of your choices. So you can read my above and determine which is false. If you have a question about any of what I said above please let me know.
Note: I guess those 0's are suppose to be infinities? I hopefully your function is .
Step-by-step explanation:
is a polynomial function which mean it has domain of all real numbers. All this sentence is really saying is that there exists a number for any value you input into
.
Now since the is a quadratic then it is a parabola. We know it is a quadratic because it is comparable to ,
.
This means the graph sort of looks like a U or an upside down U.
It is U, when .
It is upside down U, when .
So here we have so
which means the parabola is an upside down U.
Let's look at the range. We know the vertex is either the highest point (if ) or the lowest point (if
).
The vertex here will be the highest point, again since .
The vertex's x-coordinate can be found by evaluating :
.
So the y-coordinate can be found by evaluate for
:
So the highest y-coordinate is 6. The range is therefore .
If you picture the upside down U in your mind and you know the graph is symmetrical about x=-2.
Then you know the parabola is increasing on and decreasing on
.
So let's look at the intevals they have:
So on the function is increasing.
Looking on the function is increasing on (-4,-2) but decreasing on the rest of that given interval.
The function's y-intercept can be found by putting 0 in for :
The y-intercept is positive since 2>0.
