Question

Describe how to sketch the graph of y = –tan(2x) + 3 using the parent function.

Answer 1

Answer:

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Start by graphing the tangent function.

Compress the graph horizontally by making the period one-half pi.

Reflect the graph over the x-axis.

Shift the graph up 3 units.

Step-by-step explanation:

Answer 2

Transformation involves changing the size and location of a function.

The sequence of transformation from the parent function is:

• Stretch the graph horizontally by 1/2
• Reflect over the x-axis.
• Translate up by 3 units.

The function is given as:

$\mathbf{y = -tan(2x) + 3}$

The parent function is:

$\mathbf{y = tan(x)}$

First, we stretch the graph horizontally by 1/2

This gives:

$\mathbf{y = tan(\frac{x}{1/2})}$

$\mathbf{y = tan(2x)}$

Next, the graph is reflected over the x-axis.

The rule of this transformation is:

$\mathbf{(x,y) \to (x,-y)}$

So, we have:

$\mathbf{y = -tan(2x)}$

Lastly, the graph is translated up by 3 units.

The rule of this transformation is:

$\mathbf{(x,y) \to (x,y+3)}$

So, we have:

$\mathbf{y = -tan(2x) + 3}$

Hence, the sequence of transformation from the parent function is:

• Stretch the graph horizontally by 1/2
• Reflect over the x-axis.
• Translate up by 3 units.

Read more about transformations at:

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