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)

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)

Question
Performing transformations
asked 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)

Answers (1)

2020-11-23

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

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