What is the range of y = -2 cos 3x?

Mar 30, 2018

$\left\{y \in \mathbb{R} | - 2 \le y \le 2\right\}$

Explanation:

We have to know the range of a normal $\cos \left(x\right)$ function and that is 1 and -1

We next have to know what the translation form of cosine graphs looks like

$A \cos \left[B \left(x - C\right)\right] + D$

A~Amplitude, stretches all the y values by A
B~Period, stretches the period by $\frac{1}{B}$
C~ vertical translation, moves the x values across by C
D~ horizontal translation, moves the y values up D

So A and D effect the range and B and C effect the domain

So from this we know the y values have been stretched by -2 so the range becomes -2 and 2

$\left\{y \in \mathbb{R} | - 2 \le y \le 2\right\}$