MATH 131-505 Spring 2015
Review I
c
Wen
Liu
1.1
• Defintion of a function, domain of a function, range of a function. Vertical line test.
• Interval notation: difference between (a, b) and [a, b].
• Piecewise defined functions: be able to graph.
• Even functions, odd functions: how to check to see a function is even or odd.
1.2
• Be able to classify different functions based on their equations and/or shapes of their graphs.
• Defintions of polynomials, rational functions, power functions, root functions, algebraic functions, logarithmic functions, and trigonmetric functions.
• Be able to find the domain of a function.
• Be able to formulate from a word problem and interperet it.
1.3
• Know how to get new functions from old. For example: how to get −f (x) from f (x)?
• Know how to compute f ± g, f g, f /g, and f ◦ g.
1.5
• Know graph of ax .
• Know all properties of ax in order to graph, simplify, and solve equations.
1.6
• Defintion of a one-to-one function. Horizontal line test.
• Given f (x), know how to find f −1 .
• Know all properties of loga x in order to graph, simplify, and solve equations.
2.1
• Know how to find the average rate of change between two points. For example, if the distance
function s(t) is given, then the average rate of change between two points is just the average
velocity, which is (s(t2 ) − s(t1 )) /(t2 − t1 ).
• Know how to estimate the instantaneous velocity or the slope of a tangent line to a graph using
numerical approximations.
2.2
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MATH 131-505 Spring 2015
Review I
c
Wen
Liu
• Be able to find limits graphically.
• Know the difference in a limit value and a function value.
2.3
• Know the limit laws.
• Know how to compute limits by direct substitution, factor and cancel, multiply by its conjugate,
and find common denominator.
• Know how to find limits of piecewise-defined functions.
2.4
• Know the definition of discontinuity.
• Continuous from the right or from the left.
• Be able to find the discontinuities of piecewise-defined functions.
• Be able to find a, b such that the piecewise-defined function f (x) is continuous everywhere.
2.5
• Know vertical asymptotes and horizontal asymptotes and be able to read from the graph.
• Be able to use limits to find vertical asymptotes and horizontal asymptotes.
• Know how to compute the limits as x → ±∞.
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