Trigonometric Graphs

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.

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a

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.

A

Vertical translation of $\frac{\pi}{3}$π3 units up.

B

Vertical translation of $3$3 units down.

C

Horizontal translation of $3$3 radians left.

D

Horizontal translation of $\frac{\pi}{3}$π3 radians right.

A

Vertical translation of $\frac{\pi}{3}$π3 units up.

B

Vertical translation of $3$3 units down.

C

Horizontal translation of $3$3 radians left.

D

b

Determine the value of $j$`j`.

c

Determine the smallest positive value of $k$`k`.

Easy

Approx 2 minutes

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Display and interpret the graphs of functions with the graphs of their inverse and/or reciprocal functions