Mathematics 133 – Intensive Calculus for Science 1 Things to Know – Quiz 1 September 6, 2000

Recall that the first graded quiz of the semester will be given in class on Friday, September 8. There will be three or four questions similar to problems from the first problem set. You should know the following material.

1) Linear functions and their properties (Section 1.2)

a) The slope-intercept (y = mx + b) and point-slope (y − y_{0} = m(x − x_{0})) forms for linear functions

b) The meaning of the slope and how to determine it from either a formula for the

function, or from a table of values

2) Exponential functions and their properties (Section 1.3)

a) The general formula for exponential functions f(x) = ba^{x} (or using different letters, P (t) = P_{0}a^{t}, as on page 17 of the text).

b) Exponential growth versus exponential decay (which values of a give which case)

c) Be able to determine an equation for an exponential function, given a graph or a table of values.

d) How to tell exponential functions apart from linear functions

3) Power functions and their properties (Section 1.4) a) Algebraic rules for exponents

b) The general form of power functions: y = kx^{p}

c) The general shapes of their graphs.

d) Which functions grow faster as x grows: powers or exponentials?

Good Review Problems:

1) Section 1.2/11, 18

2) Section 1.3/problems like 7-9, 20-22

3) Section 1.4/problems like 1-8, 10