Find the equation for the curve in its final position. The graph y=tan(x) is shifted a distance of pi/12 to the right, stretched by a factor of 7, translated 8 units upward, then reflected in the x-axis
To find the equation for the curve in its final position, we need to apply each transformation one by one.
1. Shifting the graph a distance of pi/12 to the right:
The original equation y = tan(x) is shifted pi/12 units to the right by replacing x with (x - pi/12).
New equation: y = tan(x - pi/12)
2. Stretching the graph by a factor of 7:
We multiply the equation by the factor of 7.
New equation: y = 7 * tan(x - pi/12)
3. Translating the graph 8 units upward:
We add 8 to the equation.
New equation: y = 7 * tan(x - pi/12) + 8
4. Reflecting the graph in the x-axis:
We multiply the equation by -1 to reflect it in the x-axis.
New equation: y = -7 * tan(x - pi/12) - 8
Therefore, the equation for the curve in its final position after shifting, stretching, translating, and reflecting is y = -7 * tan(x - pi/12) - 8.