Graphs of functions--step by step, please?

Question

For each of the following functions, give the domain and a description of the graph
y= f(x) in the xy-plane, including its shape, and the x- and y-intercepts.

a) f(x) = √(x+2)
b) f(x) = x + lxl

Answer 1

a) The given fuction is f(x) = √(x+2)

Domain of f(x) is  x greater than -2

To find  X - intercepts  then y = f(x) =0

o = √(x+2) ⇒ x = -2

X - intercept  is (-2,0 )

To find Y - intercepts  then x =0 and y = f(x)

f(x) = √(x+2)

y = √2

Y - intercept  is ( 0, √2 )

The graph of the fuction is

 

 

 

 

Answer 2

b) The given fuction is f(x) = x +|x|           

Domain is all real numbers.

The function also  written as

f(x) = x +|x|

f(x) = 0 when x<0; otherwise f(x) = 2x.

To find X - intercept  then y = f(x) = 0

X - intercept  is (0, 0)

Y - intercept  is (0, 0)

The graph of the fuction is

The graph indicates straight line along the negative x-axis

and then is a step upward straight line in the first quadrant.