Name: Graphical Transformation of Trigonometric Functions
Uploaded: 2019-07-19
Duration: 1 h 7 min 57 s
Description: We love to graph functions, and now that we know about trigonometric functions, these are periodic functions. Let's learn to graph those too!

Question

Describe how to transform the graph of

y = \sin x

to

y = \sin (- 2 x) + 1

.

Accepted Answer

We are given to transform the graph of $y = \sin x$ to $y = \sin (- 2 x) + 1$ .

Translation: For the sinusoidal functions $f (x) = \sin x$ and $f (x) = \cos x, y = f (x) + d$ translates $y = f (x)$ by $d$ units in the $y$ -direction.

i) when $d > 0$ , the graph moves in the positive $y$ -direction (up).

ii) when $d < 0$ , the graph moves in the negative $y$ -direction (down).

Dilation: For the sinusoidal functions $f (x) = a \sin b x$ and $f (x) = a \cos b x$ :

i) $y = a f (x)$ is a vertical dilation of $f (x)$ , scale factor $a$ , parallel to the $y = \sin x$ -axis. $a$ is the amplitude.

ii) $y = f (b x)$ is a horizontal dilation of $f (x)$ , scale factor $\frac{1}{b}$ , parallel to the $x$ -axis. $b$ is the frequency.

Now, to transfer $y = \sin x$ to $y = \sin (- 2 x) + 1$ , we need to do the following step:

i) Draw the graph for $y = \sin x$ .

ii) Transform the graph from $y = \sin x$ to $y = \sin (2 x)$ by increasing (dilating) the frequency by a factor $2$ as shown below:

iii) The graph of $y = \sin (- 2 x)$ is obtained by taking the image of the graph $y = \sin (2 x)$ on the $x$ -axis as shown below.

iv) Shift the graph by $1$ unit upward to get the required graph of equation $y = \sin (- 2 x) + 1$ .

This is the required graph.

Describe how to transform the graph of $y = \sin x$ to $y = \sin (- 2 x) + 1$ .

Important Questions on Trigonometric Functions

Learn and Prepare for any exam you want !

Describe how to transform the graph of y=sinx to y=sin(-2x)+1.

Important Questions on Trigonometric Functions

Learn and Prepare for any exam you want !

Describe how to transform the graph of $y = \sin x$ to $y = \sin (- 2 x) + 1$ .