Calculus: Functions and Graphs flashcards

Question 1

What makes a rule from inputs to outputs a function?

Accepted Answer

Each input is mapped to exactly one output.

Question 2

What are the domain and range of a function?

Accepted Answer

The domain is the set of inputs; the range is the set of outputs.

Question 3

Which variable of a function is the independent variable?

Accepted Answer

The input variable.

Question 4

What does the vertical line test say about the graph of a function?

Accepted Answer

Every vertical line meets the graph at most once.

Question 5

How many y-intercepts can a function have?

Accepted Answer

At most one.

Question 6

What is a zero of a function f?

Accepted Answer

A real number x with f(x) = 0.

Question 7

How is the composite function g ∘ f defined?

Accepted Answer

(g ∘ f)(x) = g(f(x))

Question 8

What is the condition for f to be an even function?

Accepted Answer

f(−x) = f(x) for every x in the domain of f.

Question 9

What is the condition for f to be an odd function?

Accepted Answer

f(−x) = −f(x) for every x in the domain of f.

Question 10

What symmetry does the graph of an odd function have?

Accepted Answer

Symmetry about the origin.

Question 11

What is the degree of a polynomial function?

Accepted Answer

The largest exponent of any of its terms.

Question 12

What is the point-slope equation of a line?

Accepted Answer

y − y1 = m(x − x1)

Question 13

What is the slope-intercept form of a line?

Accepted Answer

y = mx + b

Question 14

What is the domain of a rational function p(x)/q(x), with p and q polynomials?

Accepted Answer

All x for which q(x) ≠ 0.

Question 15

What is the domain of the root function x^(1/n) when n is even?

Accepted Answer

[0, ∞)

Question 16

What is a piecewise-defined function?

Accepted Answer

A function defined by different formulas on different parts of its domain.

Question 17

What is the radian measure of a 180° angle?

Accepted Answer

π radians.

Question 18

What is the period of the sine and cosine functions?

Accepted Answer

2π

Question 19

What is the period of the tangent and cotangent functions?

Accepted Answer

π

Question 20

What property must a function have in order to have an inverse?

Accepted Answer

It must be one-to-one.

Question 21

What does the horizontal line test say?

Accepted Answer

f is one-to-one exactly when no horizontal line crosses its graph more than once.

Question 22

About which line are the graphs of f and its inverse symmetric?

Accepted Answer

The line y = x.

Question 23

Why must domains be restricted to define the inverse trigonometric functions?

Accepted Answer

Because the trigonometric functions are periodic, so not one-to-one on their full domains.

Question 24

What are the domain and range of the exponential function y = b^x?

Accepted Answer

Domain (−∞, ∞); range (0, ∞).

Question 25

For which bases b is y = b^x increasing?

Accepted Answer

b > 1

Question 26

What are the domain and range of y = log_b(x)?

Accepted Answer

Domain (0, ∞); range (−∞, ∞).

Question 27

What does y = log_b(x) mean in exponential form?

Accepted Answer

b^y = x

Question 28

What limit defines the number e?

Accepted Answer

The value that (1 + 1/m)^m approaches as m grows larger; about 2.718282.

Question 29

What is the natural logarithm ln x?

Accepted Answer

The logarithm with base e: ln x = log_e x.

Calculus: Functions and Graphs flashcards

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