Question

Describe similarities and differences between the graphs of y=2tan(x) and

y=tan(x).
a) Both have vertical stretches.
b) Both have horizontal stretches.
c) One is a reflection of the other.
d) One has a different phase shift.

Answer 1

The graphs of y=2tan(x) and y=tan(x) both have the same period and symmetry, with the primary difference being a vertical stretch in y=2tan(x), making it have higher peaks and deeper troughs. They are more similar than different.

Step-by-step explanation:

The graphs of y=2tan(x) and y=tan(x) share some similarities and differences. Here we will dive into those aspects.

• Both graphs have the same period and asymptotes since the tangent function naturally repeats every π radians (or 180 degrees) and has vertical asymptotes at odd multiples of π/2.
• Both functions are odd, meaning they are symmetric with respect to the origin which is evident in their graphs.

• The graph of y=2tan(x) exhibits a vertical stretch compared to y=tan(x), which makes the peaks and troughs of the graph twice as high or deep respectively.
• There is no phase shift or horizontal stretch difference between the two graphs; they both start their cycle at the same place on the x-axis.

When comparing the two graphs, it is clear that overall, the graphs are more similar than different. The main distinction is the vertical stretch present in y=2tan(x), which affects the amplitude of the function but does not change its fundamental shape or position on the graph.