Question

12. Graph the function. Label the vertex and axis of symmetry. State the domainand range. Then describe where the function is increasing and decreasing. *f(x) = {(x – 1)2 +3

Answer 1

we have

f(x)=(1/2)(x-1)^2+3

this is a vertical parabola open upward

the vertex is a minimum

the vertex is the point (1,3)

the axis of symmetry of a vertical parabola is equal to the x-coordinate of the vertex

so

the axis of symmetry is x=1

The domain of any parabola is all real numbers

Domain (-infinire, infinite)

The range is the interval {3, infinite)

The function is increasing at the interval (1, infinite)

The function is decreasing at the interval (-infinite, 1)

see the attached figure to better understand the problem

please wait a minute