Question

Which values complete the function? f(x) = (x – )(x ).

Answer 1

The values needed for completing the function to match with its graph is $f(x) = -(x+4)(x-3)$

How to find the function which was used to make graph?

There are many tools we can use to find the information of the relation which was used to form the graph.

• A graph contains data of which input maps to which output.
• Analysis of this leads to the relations which were used to make it.
• For example, if the graph of a function is rising upwards after a certain value of x, then the function must be having increasingly output for inputs greater than that value of x.
• If we know that the function crosses x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.

The graph of the considered problem which is missing is attached below.

Let the completed function is

$f(x) = a(x-b)(x-c)$

Then the roots of the function would be the values of x at which the function becomes 0, and they are $x = b$ and $x = c$

Since the graph crosses the x axis at -4 and 3, therefore, as the points on x axis are the roots of the functions of variable x, therefore, we get:

b and c to be -4 and 3, therefore, the function is

$f(x) = a(x-(-4))(x-3) = a(x+4)(x-3)$

Since the function crosses the y axis at y = 12, and since on y axis, the value of x is 0, therefore, putting x = 0, and equating the output to 12, we get:

$f(x) = a(x+4)(x-3)\\12 = a \times 4 \times -3\\12 = a \times -12\\\\\text{Dividing both the sides by -12}\\\\\dfrac{12}{-12} = a\\\\a = -1$

Therefore, the completed function would look like:

$f(x) = -(x+4)(x-3)$

Thus, the values needed for completing the function to match with its graph is $f(x) = -(x+4)(x-3)$

Learn more about roots of a polynomial function here:

brainly.com/question/19508384