MATA29 Calculus I for the Life Sciences - Week 1: Properties of Functions (Fill in the Blank Flashcards)

Flashcards cover core definitions, representations, and basic operations with functions, intervals, linear equations, and introductory composition from Week 1 of MATA29.

The set of all possible inputs is called the __.

domain

The set of all possible outputs is called the __.

range

A function can be represented using one or more of the following tools: a set of points, a table, a graph, or a __.

formula

The vertical line test states that a graph is a function if any vertical line intersects the graph no more than __.

once

For f(x) = x^2 − 1, f(−1) = __.

0

If g(x) = √(1 − x), g(−2) = __.

√3

h(t − 1) = __.

1/(t − 4)

f(x) + 3 = __.

x^2 + 2

f(x + 3) = __.

x^2 + 6x + 8

g(4) = __.

not a real number

The interval {x : 1 < x < 2} equals __.

(1, 2)

{x : π ≤ x < 4} equals __.

[π, 4)

{x : x < 3} equals __.

(-∞, 3)

{x : x ≥ −5} equals __.

[-5, ∞)

The real numbers set is __.

(-∞, ∞)

The interval {x : x ≤ −2} is __.

(-∞, −2]

The domain of f(x) = 3(x − 1)^2 + 5 is __.

(-∞, ∞)

For g(x) = √(9 − x) + 1, the domain is __.

(-∞, 9]

A linear function has the form __.

y = mx + b

The x-intercept occurs when y = 0, and the y-intercept occurs when x = __.

0

A line with x-intercept 4 and y-intercept −20 has slope m = __.

5

The slope of a line through (x1, y1) and (x2, y2) is m = __.

(y2 − y1)/(x2 − x1)

Δy is defined as y2 − y1 and equals the __.

rise

Δx is the __.

run

The point-slope form of a line is __.

y − y1 = m(x − x1)