Step 1 parent function

Parent function is a function that sustains the basic definition of the whole function. In other words, parent function is the root of the function which isbuild upon it.

the given function is f(x)=2|x|+3

here, the parent function in this equation is f(x)=|x|

Step 2 transformation

first the function |x| is multiplied by

f(x)=2|x|

then 3 is added to the function which lifts the graph along the y-axis by 3 units in the upward direction

f(x)=2|x|+3

Step 3 domain

The domain is the set of all values which a function can take so, in this function, all the real value can be taken hence, the domain of this function is R

Step 4 range the range is the set of all the values a function can give when we put the values of x where

\(\displaystyle{x}\in{R}\) in this equation, the range of a function is all the positive real numbers as mod changes every number into positive number.

so, \(\displaystyle{f{{\left({x}\right)}}}\in{R}^{{+}}\)

Parent function is a function that sustains the basic definition of the whole function. In other words, parent function is the root of the function which isbuild upon it.

the given function is f(x)=2|x|+3

here, the parent function in this equation is f(x)=|x|

Step 2 transformation

first the function |x| is multiplied by

f(x)=2|x|

then 3 is added to the function which lifts the graph along the y-axis by 3 units in the upward direction

f(x)=2|x|+3

Step 3 domain

The domain is the set of all values which a function can take so, in this function, all the real value can be taken hence, the domain of this function is R

Step 4 range the range is the set of all the values a function can give when we put the values of x where

\(\displaystyle{x}\in{R}\) in this equation, the range of a function is all the positive real numbers as mod changes every number into positive number.

so, \(\displaystyle{f{{\left({x}\right)}}}\in{R}^{{+}}\)