What is the period of the function f(x) shown in the graph?

What is the length of the unknown leg in the right triangle ?

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =

Graph a triangle (xyz) and reflect it over the line y=x to create triangle x’y’z’. describe the transformation using words. draw a line segment from point x to the reflecting line, and then draw a line segment from point x’ to the reflecting line. what do you notice about the two line segments you drew? do you think you would see the same characteristics if you drew the line segment connecting y with the reflecting line and then y’ with the reflecting line? how do you know?