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You have provided an image containing two sets of mathematical problems related to graphing functions. Here's a breakdown:

### Section A:
Graph the following functions:

1. \( f(x) = 2x + 1 \), \( g(x) = -2x + 1 \), and \( h(x) = 1 \) (all on one coordinate system).
2. \( f(x) = x^2 - 4x + 5 \).
3. \( f(x) = -(x - 3)^2 - 2 \).
4. \( f(x) = \frac{1}{(x+2)^2} + 3 \).
5. \( f(x) = \frac{1}{(x - 1)^3} - 1 \).
6. \( f(x) = 4^x \), \( g(x) = 4^x + 3 \) (all on one coordinate system).
7. \( f(x) = \left(\frac{1}{4}\right)^x \), \( g(x) = \left(\frac{1}{4}\right)^x - 1 \) (all on one coordinate system).
8. \( f(x) = \log_3{x} \).
9. \( f(x) = \log_{1/3}{x} \).
10. \( f(x) = 1 + \log_3{(x - 1)} \).

### Section B:
Graph the following trigonometric functions:

1. \( f(x) = \sin{x} \) for \( -\pi/2 \leq x \leq \pi/2 \) and its inverse \( f^{-1}(x) \) for \( -1 \leq x \leq 1 \) (both on one coordinate system).
2. \( f(x) = \cos{x} \) for \( 0 \leq x \leq \pi \) and its inverse \( f^{-1}(x) \) for \( -1 \leq x \leq 1 \) (both on one coordinate system).
3. \( f(x) = \tan{x} \) for \( -\pi/2 \leq x \leq \pi/2 \) and its inverse \( f^{-1}(x) \) for \( -\infty \leq x \leq \infty \) (both on one coordinate system).

Would you like me to help with a specific graph or function explanation? I can also assist in sketching or analyzing the behavior of these functions in detail.

### Follow-up questions:
1. What are the intercepts and asymptotes for the logarithmic functions in Section A?
2. How do the transformations (like vertical shifts or stretches) affect the shape of the quadratic functions?
3. Can you explain the behavior of the inverse trigonometric functions in Section B?
4. What is the domain and range for each function in Section A?
5. How do the bases in logarithmic functions influence the growth or decay rate?

### Tip:
When graphing functions with transformations (like shifts or scaling), always identify the base function first, then apply the transformations step by step for clarity.

Graph the following functions from Section A and B (various functions involving linear, quadratic, exponential, logarithmic, and trigonometric functions).

Explore the graphs of various functions, including linear, quadratic, exponential, and logarithmic functions, along with trigonometric and inverse trigonometric graphs. Suitable for high school students in Grades 10-12.

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