Question

On a coordinate plane, a curved line crosses the x-axis at (negative 1.5, 0), the y-axis at (0, negative 2), and the x-axis at (1.5, 0). Determine the domain and range of the given function. The domain is . The range is

Answer 1

Answer:

domain F(x) = All real numbers

Range F(x)  [ -2 ,  + ∞ ]

Step-by-step explanation:

There are three points of the curve

P₁ ( -1,5 , 0 )   Q ( 0. -2 ) and P₂ ( 1,5 , 0 )

We can see that P₁   and P₂  are simmetric around y axis, and point Q looks like a vertex we conclude the curve is of the form

ax² + bx + c = y

The curve is a parabola

when x = 0      y = -2     then   c  = - 2

And  plugging in the coordinates of the points in the equation we get:

a (-1,5)²  +  b (-1,5) + c = 0      ⇒  2,25*a  - 1,5*b - 2 = 0

a (1,5)²   +  b ( 1,5)  + c = 0     ⇒   2,25*a + 1,5*b -2 = 0

Adding these two equations

4.5*a - 4 = 0

a =  4/4,5

as vertex is  Q ( 0 , -2 )

x = - b/2a      ⇒   0 = - b/ 9      ⇒  b  =  0

Therefore the equation of the function is:

ax² + c = 0

(4/4,5) x² - 2 = 0

Having the equation we can determine Domain

domain F(x) = All real numbers

Range F(x)  [ -2 ,  + ∞ ]

Answer 2

Answer:

The answer for domain is all real numbers and for range it is the second option, all real numbers greater than or equal to -2.