Trigonometric Graphs

New Zealand

Level 7 - NCEA Level 2

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.

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

b

Determine the value of $j$`j`.

c

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

Easy

1min

Consider the graphs of $y=\sin x$`y`=`s``i``n``x` and $y=5\sin\left(x+\left(\left(-60\right)\right)\right)$`y`=5`s``i``n`(`x`+((−60))).

Easy

1min

Consider the graphs of $y=\cos x$`y`=`c``o``s``x` and $y=2\cos\left(x+45^\circ\right)$`y`=2`c``o``s`(`x`+45°).

Easy

< 1min

The graph of $y=\sin x$`y`=`s``i``n``x` has been transformed into the graph of $y=\sin\left(x+\left(\left(-45\right)\right)\right)-2$`y`=`s``i``n`(`x`+((−45)))−2.

Easy

1min

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