Transformations of sine and cosine curves and equations
Interactive practice questions
The functions $f\left(x\right)$f(x) and $g\left(x\right)=f\left(x-k\right)-j$g(x)=f(x−k)−j have been graphed on the same set of axes in grey and black respectively.
What transformations have occurred from $f\left(x\right)$f(x) to $g\left(x\right)$g(x)?
Select all that apply.
Horizontal translation of $\frac{\pi}{3}$π3 radians right.
Vertical translation of $\frac{\pi}{3}$π3 units up.
Vertical translation of $3$3 units down.
Horizontal translation of $3$3 radians left.
Determine the value of $j$j.
Determine the smallest positive value of $k$k.
The graph of $y=\cos x$y=cosx has been transformed into the graph of $y=\cos\left(2x+\frac{\pi}{3}\right)$y=cos(2x+π3).
Consider the graphs of $y=\sin x$y=sinx and $y=5\sin\left(x+\frac{\pi}{4}\right)$y=5sin(x+π4).
Consider the graphs of $y=\cos x$y=cosx and $y=3\cos\left(x-\frac{\pi}{4}\right)$y=3cos(x−π4).