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The graph of y=tan(x) is vertically stretched by a factor of 7, shifted a distance of 12 units to the left, reflected across the x-axis, and then translated 15 units downward. Write the equation for the curve in its final position.

Respuesta :

Step-by-step explanation:

A transformation(s) of a parent function is

[tex]f(x) = a(bx - c) + d[/tex]

where a is vertical compression/stretched or reflection

B is horinzotnal compression/stretch or reflection

C is horinzontal translation

D is vertical translation.

The parent function is

[tex]y = \tan(x) [/tex]

First, we stretched this by 7

so we have

[tex]y = 7 \tan(x) [/tex]

We need to shift this 12 units to the left so we have

[tex]y = 7 \tan(x + 12) [/tex]

We need to reflect this across x axis so we get

[tex]y = - 7 \tan(x + 12) [/tex]

We need to shift this downwards 15 so we get

[tex]y = - 7 \tan(x + 12) - 15[/tex]

or because tan is a odd function you could say

[tex]7 \tan( - (x + 12) ) - 15[/tex]

[tex]7 \tan( - x - 12) - 15[/tex]

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