What is the domain of 2-5x-x^2? and

Question

what does its graph looks like?

Answer 1

The function is f (x ) = 2 - 5x - x^2.

Domain of a function f (x) is a set of those values of x which will make the function mathematically legal or correct..certain operations like division by zero , square root of a negative number do not exist in real maths.

1. Domain excludes x - values that result in division by zero.

2. Domain excludes x - values that result in even roots of negative numbers.

The function f (x ) = = 2 - 5x - x^2 is a quadratic function.There are no rational or radical expressions, so there is nothing that will restrict the domain. Any real number can be used for x to get a meaningful output.

The domain of f (x ) = 2 - 5x - x^2 is all real numbers.

To find points pick few x - values, compute the corresponding y  values.

x	y = 2 - 5x - x^2	(x , y )
-2	y  = 2 - 5(-2) - (-2)^2 =2 + 10 - 4 = 12 - 4 = 8	(-2,8)
-1	y  = 2 - 5(-1) - (-1)^2 =2 + 5 - 1 = 7 - 1 = 6	(-1, 6)
0	y  = 2 - 5(0) - (0)^2 =2 - 0 - 0 = 2	(0,2)
-4	y  = 2 - 5(-4) - (-4)^2 =2 + 20 - 16 = 22 - 16 = 6	(-4,6)
-5	y  = 2 - 5(-5) - (-5)^2 =2 + 25 - 25 = 2	(0,2)

Graph

1) Draw the coordinate plane.

2) Plot the x intercept and coordinate pairs found in the table..

3) Connect the plotted points .

When you draw your graph, use smooth curves complete the graph.

The domain of f (x ) = 2 - 5x - x^2 is all real numbers.