Find the domain of the function.

Question

(a) Find the domain of the function. (b) Locate any intercept. (c) Graph the function.
(d) Based on the graph, find the range. (e) Is f continuous on its domain?

Answer 1

Step 1:

(c) Draw the table of different values of for

 

Graph:

  Draw the coordinate plane.

  Plot the points found in the table and connect the plotted points.

 

 

 

 

 

 

 

 

Step 2:

 (d)

All possible values of is range of a function.

Observe the graph,

The range of function is .

The range in interval notation .

(e)

The function is discontinuous at .

Solution:

(d) The range in interval notation .

(e) The function is discontinuous at .

Answer 2

Step 1:

The piecewise function is

(a)

All possible values of is domain of a function.

The domain of is all real numbers.

Step 2:

(b)

Find the intercepts

Find the -intercept by substituting .

There is no -intercept.

Find the -intercept by substituting .

The function is not defined at .

The function is defined at .

The intercept is .

Solution:

(a) The domain of is all real numbers.

(b) The intercept is .