Given the function y=f(x), such that the entire graph of the funtion is above the x-axis. Explain why the equation f(x)=0 has NO real solutions.
I have no idea please help and you don't have to give me a big explaination just something simple but covers the question
Thank you please help
2007-01-01 11:55:20 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
One idea for a function entirely above the x-axis would be a parabola. The reason is because of how it works, with the vertex. You couldn't choose f(x) to be a line in the form y = mx + b, because that will cross the x-axis (provided m > 0).
Consider the parabola f(x) = x^2 + 9. I can guarantee you that this does NOT cross the x-axis. The graphical representation would be a parabola, with its vertex being at (0, 9), facing upward.
Since it doesn't cross the x-axis, then we should not get any solutions for f(x) = 0. Let's show this algebraically.
f(x) = 0 means
x^2 + 9 = 0. Moving the 9 to the right hand side, we get
x^2 = -9
And we CANNOT take the square root of both sides to obtain (real) solutions for x. This is not surprising, since the graph does not cross the x-axis.
Hope that helps.
2007-01-01 12:00:59 · answer #1 · answered by Puggy 7 · 0⤊ 0⤋
Okay, basically f(x) is the same thing as y.
So why does the equation y=0 have no real solutions?
Well, first of all a solution to this equation would be the x-value that corresponds with the y-value being 0. In simpler terms, the solution would be the x in the coordinate (x,0).
Let's take the point (1,0). If you plot it do you see that it lies on the x-axis? Same with (2,0) and so on. Any point (x,0) on any function lies on the x-axis. Therefore, any function with the point (x,0) touches the x-axis.
But this function lies ABOVE the x-axis, therefore no point on it would touch the x-axis. Therefore, there is no x-value for which the y-value is 0. There is no real solution.
2007-01-01 20:04:19 · answer #2 · answered by teekshi33 4 · 0⤊ 0⤋
If the entire graph is ABOVE the X-axis, than all y values have to be greater than 0 (>0). Therefore, if you are setting f(x) = 0, you will find that there are no REAL solutions to this because the graph never goes through y=0 since it is ALWAYS above the x-axis.
2007-01-01 19:59:29 · answer #3 · answered by joe_jenninz 2 · 0⤊ 0⤋
This seems straightforward.
If the entire graph lies above the x axis, that means that for all values of x, f(x) is a positive number (the area of the graph above the x asix).
then f(x) > 0 for all values of x.
So there is NO value of X for which f(x) = 0, otherwise the graph would "touch" the x axis at this point.
2007-01-01 19:59:40 · answer #4 · answered by firefly 6 · 0⤊ 0⤋
by definition if all values of f(x) are above the X-axis
The X-axis is also where y(aka f(x)) is equal to 0
since this does not ever occur then there can be no solution to
f(x)=0
2007-01-01 19:59:18 · answer #5 · answered by beanie_boy_007 3 · 0⤊ 0⤋
f(x) will never be ZERO since it stays always above x-axis.
So f(x) = 0 is not achievable, a solution for roots of x is not possible.
2007-01-01 20:00:23 · answer #6 · answered by Sheen 4 · 0⤊ 0⤋