Answered: "Functions f and g are graphed in the..."

High School
Geometry
High school geometry
Performing transformations

illusiia

Answered question

2020-11-22

Functions f and g are graphed in the same rectangular coordinate system. If g is obtained from f through a sequence of transformations, find an equation for g.
(Graph given on the link)

Answer & Explanation

lobeflepnoumni

Skilled2020-11-23Added 99 answers

Given:
The graph of $f (x) = s q r t (16 - x^{2})$
To determine :
The equation of transformed graph shown in the given figure.
The parent graph of $f (x) = s q r t (16 - x^{2})$ .
Since the graph is shifted vertically down by 1 unit.
Therefore, the equation becomes,
$f (x) = s q r t (16 - x^{2}) - 1$
Also, the graph is a reflected graph in the x - axis . Hence we have
$f (x) = s q r t (16 - x^{2}) - 1$
Now, the graph is has a vertical compression by 4 units.
Therefore, the transformed graph is $f (x) = - 1 / 4 s q r t (16 - x^{2}) - 1$

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