domain, range of a function

Question

Find the domain of y=4(6x-9)^2.

Answer 1

The function y = 4(6x - 9)^2

We first put the equation in to the form for a translated parabola y = a (x - h )^2 + k .

Center (h, k ).

In the next step we factored 36 from the right hand side to make the coefficient of our x  "+1" as this is the standard form.

y  = 4*36(x - 9/6)^2

y  = 144(x - 9/6)^2

y  = 144(x - 1.5)^2

The above function represents a parabola vertex form  y = a (x - h )^2 + k .

 a  = 144 , h  = 1.5 and k  = 0.

a  is positive number the parabola opens up and has minimum value.

When the parabola opens up it has a minimum point which is the vertex of parabola (1.5, 0)

We know that domain of the function is all possible x  values and range is all posible y  values.

 parabola domain x  =  all real numbers.

In the minimum point y  = 0  so the graph of parabola cannot be lower than 0.

Thus the range of function y  ≥ 0.

Domain of function is all real numbers.

Range of the function is  {y |y  ≥ 0}.