Find the domain and the range of the function.

Question

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function (for example, y = x²) and show all stages. Be sure to show at least three key points. Find the domain and the range of the function.

f (x) = x² - 1

Answer 1

Step 1:

The function is  .

Obtain the graph of  from basic function ,subtract from each -coordinate on graph of basic function.

Choose random values for and find the corresponding values for .

Step 2:

Graph:

Draw the the coordinate plane.

Plot the points of the basic function 

Connect these points with a smooth curve.

Plot the points of the are

Connect these points with smooth curve.

Comments

contd...

Graph:

.

The graph of is identical to except that it is vertically shifted down 1 unit.

Step 3:

The domain of the is all real numbers.

Domain of f  in the interval notation: .

Range of  is

Range of f  in the interval notation: .

Solution:

Domain  of f  in the interval notation: .

Range  of f  in the interval notation: .