Find the equation for the curve in its final position. The graph y=sec(x) is shifted a distance of pi/4 to the left, reflected in the x-axis, then translated 7 units upward
To find the equation for the curve in its final position, we need to apply the described transformations step by step.
Step 1: Shift a distance of π/4 to the left:
The original equation is y = sec(x). Shifting it π/4 to the left means we replace x with (x + π/4). The equation becomes y = sec(x + π/4).
Step 2: Reflect in the x-axis:
To reflect in the x-axis, we need to multiply the entire equation by -1. The equation becomes y = -sec(x + π/4).
Step 3: Translate 7 units upward:
To translate upward, we add 7 to the equation. The final equation becomes y = -sec(x + π/4) + 7.
Therefore, the equation for the curve in its final position is y = -sec(x + π/4) + 7.