Question

Identify the domain and range of the function f(x) = 2x2 − 6x − 9.

Answer 1

D: ℜ

R: y ≥ −13.5

Explanation:

Determine whether the graph has a maximum or minimum value.

Since the a-value is positive, the graph opens upward and has a minimum value.

Find the x-value of the vertex.

Find the y-value of the vertex, f(1.5).

f(1.5) = 2(1.5)2 − 6(1.5) − 9

= 2(2.25) − 9 − 9

= 4.5 − 9 − 9

= −13.5

Therefore, the minimum value is −13.5.

The domain of the function is the set all real numbers, or D: ℜ.

The range is all y-values greater than or equal to −13.5, or R

Answer 2

range is the y values or ouputs
domain is inputs or x vvalues

we can use any x value
but at a certain y value, w can't go below that
find thatminimum
find the vertex
for
ax^2+bx+c
the x value of the vertex is
-b/2a
plug that in to the equaiton to get the y value

-b/2a=-(-6)/(2*2)=6/4=3/2

plug that in
2(3/2)^2-6(3/2)-9
2(9/4)-9-9
9/2-18
4.5-18
-13.5

domain=all real numbers
range=from -13.5 to positive infinity