3. Functions and Graphs Flashcards
Any set of ordered pairs is called a/an ______. The set of all first components of the ordered pair is called the ______. The set of all second components of the ordered pairs is called the _______.
relation
domain
range
A set of ordered pairs in which each member of the set of first components corresponds to exactly one member of the set of second components is called a/an ______.
function
The notation f(x) describes the values of ____ at _____.
f
x
True or false: y = x² – 1 defines y as a function of x.
True
True or false: y = ± (√x² – 1)
false
If f(x) = x² – 5x + 4, we can find f(x + 6) by replacing each occurence of ______ by ______.
x
x + 6
The graph of a function is the graph of its _______.
ordered pairs
If any vertical line intersects a graph ______, the graph does not define y as a/an ______ of x.
more than once
function
If the x-intercepts of a function are –1 and 3, then f(–1) = _____ and f(3) = _____. The x-intercepts, –1 and 3, are called the ______ of the function.
0
0
zeros
True or false: A function can have more than one y-intercept.
false
Assume that f is a function defined on an open interval I and x1 and x2 are any elements in the interval I.
f is increasing on I if f(x1) _______ when x1 < x2.
f is decreasing on I if f(x1) _______ when x1 < x2.
f is constant on I if f(x1) _______.
< f(x2)
> f(x2)
= f(x2)
If f(a) > f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative _______ of f.
maximum
If f(a) < f(x) in an open interval containing a, x ≠ a, then the function value f(a) is a relative _______ of f.
minimum
The graph of an equation is symmetric with respect to the _____ if substituting –x for x in the equation results in an equivalent equation.
y-axis
The graph of an equation is symmetric with respect to the _____ if substituting –y for y in the equation results in an equivalent equation.
x-axis
The graph of an equation is symmetric with respect to the _____ if substituting –x for x and –y for y in the equation results in an equivalent equation.
origin
If f is an even function, then f(–x) = _______. The graph of an even function is symmetric with respect to the ______.
f(x)
y-axis
If f is an odd function, then f(–x) = ______. The graph of an odd function is symmetric with respect to the ______.
–f(x)
origin
A function defined by two or more equations over a specified domain is called a/an _______ function.
piecewise
The greatest integer function is defined by int(x) = the greatest integer that is _______.
For example: int(2.5) = \_\_\_\_ int(–2.5) = \_\_\_\_ and int(0.5) = \_\_\_\_\_.
less than or equal to x
2
–3
0
The expression
[f(x + h) – f(x)] / h, h ≠ 0,
is called the _______ of the function. We find this expression by replacing x with ______ each time x appears in the function’s equation. Then we subtract ______. After simplifying, we factor _____ from the numerator and divide out identical factors of ______ in the numerator and denominator.
difference quotient
x + h
f(x)
h
h
True or false: f(x + h) = f(x) + h
false
True or false: f(x + h) = f(x) + f(h)
false
Data presented in a visual form as a set of points is called a/an ______. A line that best fits this set of points is called a/an ______ line.
scatter plot
regression
The slope, m, of a line through the distinct points (x1, y1) and (x2, y2) is given by the formula m = ______.
(y2 – y1) / (x2 – x1)
If a line rises from left to right, the line has _____ slope.
positive
If a line falls from left to right, the line has _____ slope.
negative
The slope of a horizontal line is _____.
zero
The slope of a vertical line is ______.
undefined