Question

Start with f(x) = cos(x).
Hint: Make sure you got the correct function by graphing it on some electronic gadget.
a) Define fA(x) so that cos is translated up by 2.
b) Define fB(x) so that cos is translated down by 2.
c) Define fC(x) so that cos is translated right by π.
d) Define fD(x) so that cos is translated left by π.

Answer 1

Start with $f(x) = \cos(x)$ .

Hint: Make sure you got the correct function by graphing it on some electronic gadget.

a) Define $fA(x)$ so that $\cos$ is translated up by 2.

$\mathsf{fA}(\mathsf{x}) = \mathsf{cos}(\mathsf{x}) + 2.$

b) Define $fB(x)$ so that $\cos$ is translated down by 2.

$\mathsf{fB}(\mathsf{x}) = \cos (\mathsf{x}) - 2$

c) Define $fC(x)$ so that $\cos$ is translated right by $\pi$ .

$\mathsf{fC}(\mathsf{x}) = \cos (\mathsf{x} + \pi)$

d) Define $fD(x)$ so that $\cos$ is translated left by $\pi$ .

$\mathsf{fD}(\mathsf{x}) = \cos (\mathsf{x} - \pi)$