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 (

Question

2 years ago

15

1.5, 0).
Determine the domain and range of the given function.

The domain is
all real numbers
.

The range is
.

1 answer:

Lisa [10] · Answer 1 · 2023-01-27T20:09:32+03:00

Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]

<h3>What is the domain and range of a function?</h3>

A domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

The curve points are

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

We can see that P₁ and P₂ are symmetric around the y-axis, and point Q looks like a vertex so we can conclude the curve as

ax² + bx + c = y

The curve is a parabola

when x = 0

y = -2

then c = - 2

The equations we get,

a (-1.5)² + b (-1.5) + c = 0

2.25a - 1.5b - 2 = 0

a (1.5)² + b ( 1.5) + c = 0

2.25a + 1.5b -2 = 0

Adding these two equations

4.5a - 4 = 0

a = 4/4.5

The vertex is Q ( 0 , -2 )

x = - b/2a

0 = - b/ 9

b = 0

Therefore the equation of the function :

ax² + c = 0

(4/4.5) x² - 2 = 0

Therefore, Domain F(x) = All real numbers and the Range F(x) [ -2 , + ∞ ]

Learn more about appropriate domain here:

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