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Let g (x) be the indicted transformation of f (x) = - I3xl -4. Stretch the graph of f (x) = - l3xl - 4 vertically by a factor of 3 and reflect it across the x-axis. Identify the rule and graph of g (x).

Let g x be the indicted transformation of f x I3xl 4 Stretch the graph of f x l3xl 4 vertically by a factor of 3 and reflect it across the xaxis Identify the ru class=

Respuesta :

we have the parent function f(x)

[tex]f\left(x\right)=-\left|3x\right|-4[/tex]

step 1

Stretch the graph of f (x) vertically by a factor of 3

The rule is given by

(x,y) --------> (x,3y)

so

[tex]-\left|3x\right|-4----->\text{ }-3\left|3x\right|-12[/tex]

step 2

Reflection across the x-axis

The rule is given by

(x,y) -------> (x,-y)

so

[tex]-3\left|3x\right|-12\text{ -----> }3\lvert3x\rvert+12[/tex]

therefore

The function g(x) is

[tex]g\left(x\right)=3\left|3x\right|+12[/tex]

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