Dicenso midterm Key Concepts/Vocabulary
log(a)1
0
log(a)a
1
the maximum value of y= sinx, π <= x <= 2π, is _________ and occurs at x = ____________
1, π/2
cosine
Domain is all real numbers and the range is all real numbers from -1 to 1 inclusive
True
Even functions have graphs that are symmetric with respect to the origin
only two data points are required by a graphing utility to find the sine function of best fit ( t or f)
False
True
Function f has a local maximum at C if there is an open interval I containing C so that for all the x in I, F(x) <= f(c)
(g-f)x
If f(x) = x +1 and g(x) = x^3, then _______ = x^3 - (x+1)
5,-3
If the point (5,-3) is on the graph of f, F(___) = ______
false
If theres no domain for the function f, then the domain of f is taken to the set of all real numbers
alog(a)^M
M
y
Suppose that the graph of the function f is known. The the graph of y= f(-x) may be obtained by a reflection over the _____ axis of the graph of the function f.
Horizontal, right
Suppose that the graph of the function f is known. Then the graph of y=f(x-2) may be obtained by a _____ shift of the graph of f and the graph of x to the ____ distance of two units.
Vertical, up
Suppose that the graph of the function g is known. The graph of y =g(x) +2 may be obtained by a _____ shift of the graph of g ______ a distance of two units.
True
The cube function is odd and increasing on the interval (-infinity, infinity), true or false
False
The cube root function is odd and is decreasing on the interval (-infinity, infinity), true or false
False
The domain and range of the set in a reciprocal function is all real numbers. True or false
false
The domain f(x) = x^2 - 4 / x is { x | x =/ +/- 2}
true
The domain of (f o g) (x) consists of numbers x in the terms of f and g
(-infinity,0)
The function f(x) = x^2 is decreasing on the interval ____________.
false
The graph of the function y=F(x) always crosses the y axis
True
The graph of y=-f(x) is a reflection about the x-axis of the graph of y=f(x). True or false
true
The independent variable is sometimes referred to as the argument of function
True
The only even trigonometric functions are cosine and secant. (T or F)
Range
The set of all images of elements in the domain of a function
true
The y intercept of the graph of the function y= F(x) whose domain is all real numbers, if F(0)
False (left)
To obtain the graph of f(x) = sqrt(x+2), shift the graph of y = sqrt(x) horizontally to the right 2 units. True or false
True
To obtain the graph of f(x) = x^3 + 5, shift the graph of y= x^3 vertically up 5 units. True or false
the graph of y =sinx and y = cosx are identical except for horizontal shift (t or f)
True
the graphs of y = tanx, y=cotx, y = secx, y = cscx each have infinitely many vertical assymptoes (t or f)
True
Piecewise Functions
When functions are defined with more than one equation they are called ___________.
y=Asin(wx), has amplitude of 3 and a period of 2. a = _____________________ w = ____________________
a = 3 w = π
the function y =3cos6x a = __________________ w = _________________
a = 3 w = 1/3
false
a function can have more than one y intercept
True
a function f is decreasing on an open interval I if for any choice x1 and x2, X1 < x2, we have F(x1), < F(x2)
even, odd
an ________ function f is one for which f(-x) = f(x) for every x in the domain of f; an _____ function of f is one for which f(-x) = - F(x) for every x in the domain of f
1 Pythagorean principle
cos^2ϴ + sin^2ϴ = 1
odd (has negative answer)
cosecant of negative ϴ
Even (positive answer)
cosine of negative ϴ
3 Pythagorean principle
cot^2ϴ + 1 = csc^2ϴ
odd ( negative as answer)
cotangent of negative ϴ
sine
domain is all real numbers and the range is all real numbers from -1 to 1, inclusive
all real numbers except odd multiples of π/2 (90 degrees)
domain of tangent function is _________
cosecant
domain: all real numbers except integer multiples of (180 degrees) range: all real numbers greater than or equal to 1 or less than or equal to -1
cotangent
domain: all real numbers except integer multiples of π(180 degrees) range: all real numbers
tangent
domain: all real numbers except odd integer mutiples of π/2 (90 degrees) Range: all real numbers
secant
domain: all real numbers except odd integer mutiples of π/2 (90 degrees) Range: all real numbers greater than or equal to 1 or less than or equal to -1
for y=2sin(πx), the amplitude is 2 and the period is π/2 (t or f)
false
a = -2
find a so that the point (-1,2) is on the graph of F(x) = ax^2+4
increasing
function f -------- on an open interval I if nay choice of x and y I1 with x1>x2, F(x1) < F(x2)
independent, dependent variable
if the fuction is defined as the equation y= F(x), x is called __________ and the y is called___________
log (a)MN =
log(a)M + log (a)N
the graph of y = tanx is symmetric with respect to the __________ and has vertical asymptotes at __________
origin, odd multiples of pi/2
the graph of y = a sin (omega x - phi, the number phi/omega is called __________________
phase shift
all real numbers from -1 to 1 inclusive
range of sine function is ___________.
False
sec ϴ = 1/ sinϴ (t or f)
Even (positive answer)
secant of negative ϴ
odd (has negative as answer)
sine of negative ϴ
2π
sine, cosine, secant, cosecant all have a period of ________________.
2 Pythagorean principle
tan^2ϴ + 1 = sec^2ϴ
odd (negative answer)
tangent of negative ϴ
[0,5]
the domain F is all real numbers in the interval of [0,7], and the domain of G is all real numbers in the interval of [-2,5] and the domain of (f+g) is all real numbers in the interval of _________________
cannot equal (=/), f, g
the domain of f/g consists of numbers x for which g(x) _____ 0 and that are in the domains of both ______ and __________
vertical line
the set of points in the x-y plane is the graph of the function if and only if every ________ intersects once
π
the tangent and cotangent all have a period of _________
periodic properties for tan and cot
trig function (ϴ + π) or (ϴ + 180)
periodic properties for sin csc sec cos
trig. function (ϴ +2π) or trig. function (ϴ + 360)
the graph of the sine function has infinitely many x intercepts (t or f )
true
y = secx is symmetric to ___________ and has vertical asymptotes at __________
y-axis, odd multiples of pi
its easiest to graph y=secx by sketching the graph of ________________
y= cosx
