High School Pre-Calculus Tangent Transformations Practice Quiz

📚 Topic Summary

Tangent transformations build upon your knowledge of the basic tangent function, $y = \tan(x)$. We can manipulate this function using transformations such as vertical stretches/compressions (amplitude changes), horizontal stretches/compressions (period changes), vertical shifts, and horizontal shifts (phase shifts). The general form of a transformed tangent function is $y = A \tan(B(x - C)) + D$, where $A$ affects the vertical stretch, $B$ affects the period, $C$ represents the phase shift, and $D$ represents the vertical shift. Understanding how each parameter affects the graph is crucial for sketching and analyzing tangent functions. Remember that the period of $y = \tan(x)$ is $\pi$, but the period of $y = \tan(Bx)$ is $\frac{\pi}{|B|}$.

This quiz will test your understanding of these transformations. Good luck!

🔤 Part A: Vocabulary

Match the term with its definition:

1. Term: Period
2. Term: Amplitude (Vertical Stretch)
3. Term: Phase Shift (Horizontal Shift)
4. Term: Vertical Shift
5. Term: Asymptote

Definitions:

1. The vertical distance from the midline of the function to the maximum or minimum value.
2. A vertical line that the function approaches but never touches.
3. The horizontal displacement of the function from its original position.
4. The vertical displacement of the function from its original position.
5. The horizontal distance required for the function to complete one cycle.

✍️ Part B: Fill in the Blanks

Complete the following paragraph with the correct terms:

The general form of a transformed tangent function is $y = A \tan(B(x - C)) + D$. The parameter $A$ affects the __________ of the function. The parameter $B$ affects the __________, which is calculated as $\frac{\pi}{|B|}$. The parameter $C$ represents the __________, and the parameter $D$ represents the __________.

🤔 Part C: Critical Thinking

Explain how changing the value of 'B' in the tangent transformation equation $y = A \tan(B(x - C)) + D$ impacts the graph of the function. Be sure to discuss specific effects on the period, and include an example.