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Ronch [10]
3 years ago
12

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.
Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
6 0

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

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