Question

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.

Answer 1

Step-by-step explanation:

A transformation(s) of a parent function is

$f(x) = a(bx - c) + d$

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

$y = \tan(x)$

First, we stretched this by 7

so we have

$y = 7 \tan(x)$

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

$y = 7 \tan(x + 12)$

We need to reflect this across x axis so we get

$y = - 7 \tan(x + 12)$

We need to shift this downwards 15 so we get

$y = - 7 \tan(x + 12) - 15$

or because tan is a odd function you could say

$7 \tan( - (x + 12) ) - 15$

$7 \tan( - x - 12) - 15$