Here is a transcription and breakdown of the problems from the image you uploaded:

1. Solve the following inequalities and express the solution set in three notations (interval notation, set notation, and on a number line):

a. $x^2 - 2x + 2 \leq 6x - x^2 - 3$ b. $|2x + 3| > |x - 3|$

2. If $f(x) = x^2$, sketch the graph of the function $g(x) = 3x^2 - 12x + 16$ by transforming the graph of $f(x)$.

3. Given $f(x) = \frac{2x}{x - 3}$ and $g(x) = \sqrt{2x} - 5$, determine $(f \circ g)(x)$ and the domain $D_{f \circ g}$.

4. Prove that $\lim_{x \to 2} 3x + 2 = 8$.

5. Compute $\lim_{t \to 0} \frac{\sin(2t) + 5t}{t \cdot \sec(t)}$.

6. Determine the horizontal and vertical asymptotes of the function:

a. $f(x) = \frac{6x^2 - 30x + 36}{2x^2 - 2x - 12}$

7. Determine where the following function is not continuous: