UK Secondary (7-11)

Transformations of sine and cosine curves and equations

The graph of $f\left(x\right)$`f`(`x`) and $g\left(x\right)=f\left(x-k\right)-j$`g`(`x`)=`f`(`x`−`k`)−`j` are displayed on the same set of axes in grey and black respectively.

Loading Graph...

a

What transformations have occurred from $f\left(x\right)$`f`(`x`) to $g\left(x\right)$`g`(`x`)? Select all that apply.

Vertical translation of $60$60 units up.

A

Horizontal translation of $3^\circ$3° left.

B

Horizontal translation of $60^\circ$60° right.

C

Vertical translation of $3$3 units down.

D

Vertical translation of $60$60 units up.

A

Horizontal translation of $3^\circ$3° left.

B

Horizontal translation of $60^\circ$60° right.

C

Vertical translation of $3$3 units down.

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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