Find the equation of the line satisfying the following:

1. The line going through the point (0,5) with slope 3.

2. The line going through the two points (0,5) and (5,0).

3. The line going through the point (0,5) which is parallel to the line $y = 3x+10$.

4. The line through the points (0,5) and (0,10).

5. Draw a simple sketch with all 4 lines on it.

Sketch a graph of the following functions. The graphs are hopefully familiar. Recall how you sketch a transformation of a graph.

1. The parabolas $x^2$, $x^2 + 4$ and $(x+4)^2$.

2. The square root function $\sqrt{x}$ and $\sqrt{x+2}$

3. The cubics $x^3$ and $x^3 + 5$

4. The absolute value $|x|$ and $|x+5|$,

5. The sine function $\sin(x)$ and $5 \sin(x)$.

Simplify the following algebraic expressions.

1. $x^5 x^6 x^7$

2. $(x^5 x^6)^7$

3. $x^{-5}x^{6}x^{-7}$

4. $x^5 x^{1/6} x^{1/7}$

5. $5^x x^6 7^x$

6. $$\frac{x^2 + 2}{x^3 + 3} - \frac{x}{x^2+1},\quad \frac{x^5 + x^6}{x^7},\quad \frac{5^x + 6^x}{x^7}$$

Let $f(x) = x^2$, $g(x) = \sqrt{x}$ and $h(x) = 1/x$. Simplify the following.

1. $f(5) + g(9)$

2. $f(x)+2$

3. $f(x+2)$

4. $h(1/10)$

5. $h(g(16))$.

6. $f(h(g(16)))$

7. $(f(x+h) - f(x))/h$