Question

Can you help me about the characteristics of the function
The parabola is opening upwards, I believe the vertex is at 7, the other points are at 1.5, 0 and 4.5, 0 along the x and at 7 along the y, what is the Domain and Range, what is the end behavior and is the y axis (0,7) or (7,0)

Answer 1

So if x approaches -♾️ what does f(x) approach and if x approaches ♾️ what does f(x) approach please

Answer 2

The function you are describing is a quadratic function in the form of y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.

Given that the vertex is at (7, 0) and the other points are (1.5, 0) and (4.5, 0), we can determine that the equation of the parabola is y = a(x-7)^2.

To find the value of 'a', you can use one of the other points on the parabola. Let's use the point (1.5, 0):

0 = a(1.5-7)^2
0 = 28.25a
a = 0

Therefore, the equation of the parabola is y = 0.

The parabola in this case is a horizontal line passing through y = 0, so it does not have any end behavior. The domain of the function is all real numbers (negative and positive infinity) since the parabola extends infinitely in both directions along the x-axis. The range of the function is {0} since the graph of the function only intersects the y-axis at y = 0.

In conclusion, the y-axis in this case is (0, 7).

Answer 3

Since the function is a horizontal line passing through y = 0, as x approaches negative infinity or positive infinity, the function f(x) will approach 0.

So, as x approaches negative infinity, f(x) approaches 0, and as x approaches positive infinity, f(x) also approaches 0.