Can you give question for precalculus test for practice

Certainly! Here are five practice questions for a Precalculus test, covering a range of topics such as functions, trigonometry, and sequences.

### 1. **Function Transformations:**
   Given the function \( f(x) = \sqrt{x+4} \), write the equation for the transformed function if it is reflected over the x-axis, shifted 2 units left, and 3 units up.

### 2. **Trigonometric Identities:**
   Prove the following trigonometric identity:
   \[
   \sin^2(x) + \cos^2(x) = 1
   \]

### 3. **Exponential and Logarithmic Functions:**
   Solve the following equation for \( x \):
   \[
   3^{2x+1} = 81
   \]

### 4. **Sequences and Series:**
   Find the sum of the first 10 terms of the arithmetic sequence with the first term \( a_1 = 5 \) and the common difference \( d = 3 \).

### 5. **Conic Sections:**
   Write the equation of a circle with center at \( (-2, 3) \) and radius 5. Then, determine if the point \( (1, 7) \) lies on the circle.

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### Tip:
Remember, in Precalculus, understanding how transformations affect the graph of a function is essential. Practice visualizing how each type of transformation changes the function's graph.

### Related Questions:
1. How does reflecting a function over the y-axis affect its equation?
2. Can you derive the double angle identity for sine?
3. How do you convert from logarithmic form to exponential form?
4. What is the general formula for the nth term of a geometric sequence?
5. How do you find the distance between two points on a coordinate plane?

Would you like detailed solutions for any of these problems or have any questions?

Can you give question for precalculus test for practice?

Practice key precalculus topics with these five questions, covering function transformations, trigonometric identities, exponential and logarithmic functions, sequences, and conic sections. Perfect for students in Grades 10-12 looking to prepare for exams.

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