Key to "State the parent function, transformations, domain and range."

kzae220o3

Answered question

2021-11-23

State the parent function, transformations, domain and range.

hotcoal3z

Beginner2021-11-24Added 16 answers

Step 1
Given,

f (x) = 2^{(x - 3)} + 2

The graph of f(x) is as shown :

Step 2
Parent function:

2^{x}

Transformation :
1.Right shift by 3
2.Vertical shift of +2
Domain, D:

(- \infty, \infty)

lim_{X \to - \infty} f (x) = lim_{x \to - \infty} (2^{x - 3} + 2) = 2

lim_{X \to \infty} f (x) = lim_{x \to \infty} (2^{x - 3} + 2) = \infty

Range,R:

[2, \infty)

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