State the parent function, transformations, domain and range. 19610701501.jpg

vetrila10 2021-11-22 Answered
State the parent function, transformations, domain and range.
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Expert Answer

Robert Harris
Answered 2021-11-23 Author has 214 answers
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
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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, \(\displaystyle{f{{\left({x}\right)}}}\in{R}^{{+}}\)
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