MATH 121 – Test #1 Study Guide
Section 1.1
 familiarity with the basics (definition of function, vertical line test)
Section 1.2
 know basic shapes of quadratic and cubic functions, power and root functions, sin, cos
and tan functions
 apply transformations on p. 17 to basic graphs
Section 1.3
 state and give an intuitive explanation of the definition of limit (p. 2) (as well as left
and right-handed limits) [do not need to know the formal definition on p. 31]
 identify where limits of a given function do not exist (vertical asymptotes, certain
piecewise functions)
Section 1.4
 calculate limits using: limit laws (pp. 35 & 36), direct substitution, algebra to avoid the
“zero division problem,” the squeeze theorem
 know lim x→0 sin x / x = 1 and apply to evaluate other limits (#43–48 on p.45)
Section 1.5
 state definition and give intuitive explanation of continuity (p. 46)
 gives example of three type of discontinuities (removable, jump and infinite)
 state the intermediate value theorem and apply it to determine whether a function has a
root between two given values of x. [recall that a is a root of f(x) if f(a)=0]
 [EXTRA CREDIT] use method of bisections to estimate a root
Section 1.6
 evaluate limits at infinity: lim x→a f(x) → ∞
 evaluate infinite limits: lim x→∞ f(x) = L
 know which of the above corresponds to vertical asymptotes and which to horizontal
asymptotes
Section 2.1
 compute and interpret instantaneous rate of change (e.g., velocity) vs. average rate of
change; which relates to the slope of a secant line? which to the slope of a tangent line?
 compute derivative of a function at a point (and interpret)
Section 2.2
 know definition of derivative function f’(x) (p. 83) and compute f’(x)
 what does the derivative function tell you about f(x)?
 f’(x) negative 
negative slope

f(x) decreasing
 f’(x) positive 
positive slope

f(x) increasing
 f’(x) = 0

tangent is horizontal (zero slope)

f(x) neither increasing nor decreasing
 identify points where a function’s derivative is undefined, both graphically and
algebraically