Here are some problems for practicing some of the basic skills that we need to do well in calculus.
Knowing what are notation means is really important. Let $f(x)$ and $g(x)$ be defined by the following:
Evaluate the following:
$$f(2),\quad f(3),\quad g(f(2)),\quad f(g(2))$$
The difference quotient is the key to derivatives:
$$\frac{f(x+h) - f(x)}{h}$$
Compute and simplify the difference quotient for the following functions:
$$f(x) = x^{1/2}, \quad f(x) = x^2 - 2x,\quad f(x) = x^3$$
More challenging are these difference quotients: (you need to know the formulas to allow you to simplify)
$$f(x) = \ln(x),\quad f(x) = \sin(x)$$
Identifying composition is very important too. Write the functions $h(x)$ as a composition of two functions $f(g(x))$:
$$h(x) = (x^2 - 1)^{1/2}, \quad h(x) = \sin(2x+5),\quad h(x) = \frac{2}{x^2 - 1}$$
(There is certainly more than 1 correct answer)
Finding equations of lines is very important.
Find the equation of the line through $(1,6)$, $(10,3)$.
FInd the equation of the line that intersects the graph of $f(x) = x^2 +1$ at $x = 2$ and $x = 3$.
Find the equation of the line tangent to the graph of $f(x) = x^2 + 1$ at $x=2$. (It has slope 4).