Domain and Range
Find the domain of f(x) = 1/x + sqrt (x+5)
[-5, 0) U (0, infinity)
Given f(x) =
sqrt(x)+1
, find the inverse and the domain and range of the inverse
f-1(x)=(x-1)2, domain: [1,infinity),
range: [0,infinity]
Which of the following are true statements
A). In geometry two angles which are adjacent and congruent form a linear pair
B). In the composition of functions the output of one function becomes the input of another
C). (sqrt(10i))(sqrt(10i))=sqrt(100i^2)=10i
D).In an isosceles trapezoid the opposite angles are congruent, but the base angles are supplementary
E). The function x = y2 is symmetric with respect to the x-axis
A). false (the are adjacent and supplementary)
B). true by definition
C). false
D). true
E). The is not a function because it fails the vertical line test
Given the points (-24,8) lie on the graph of f (x,y) What will be the new coordinates on the graph of
-2 f[-3(x+6)] - 5
For the x-coordinate we reflect over the y-axis =24, multiply by (1/3) =8, then shift left 6 units = 8 + (-6) = 2.
For the y-coordinate we reflect over the x-axis, -8, multiply by 2= -16 and shift 5 units downward, given us -21. Therefore, we have (2, -21)
Which of the following are true
A). If two lines are cut by a transversal, then alternate interior angles are supplementary
B). In a circle an inscribed angle is equal to the intercepted arc
C). A square has four lines of symmetry
D). the diagonals of a rhombus are equal, but the diagonals a rectangle are perpendicular
E). If two triangles are similar, the ratio of their perimeters is the same as the scale factor
Parts C and E are both true
Find the domain of f(x)=(sqrt(x-10))/(x-18)
[10,18) U (18, +infinity)
Find the inverse of: f(x) =(5x+2)/(x-3)
f-1(x)=(3x+1)/(x-5)
Simplify (2x-1)/(x+1)*(x^2-1)/(2x^2-7x+3 , find the inverse of the resulting fraction and state the domain and range of the inverse
The resulting fraction is f(x)=(x-1)/(x-3).
f(x)=(x-1)/(x-3), f-1(x)=(3x-1)/(x-1)
domain of f-1(x) = (-infinity,1)U(1,+infinity)
range of f-1(x)=(-infinity, 3)U(3, +infinity)
Given the equation f(x) = x2, explain the transformation of h(x)= -(x-5)2+4 in words.
the graph of h is a horizontal shift of 5 units to the right, a reflection in the x-axis, followed by an upward shift of 4 units
Which statements are false
A). The diagonals of a rectangle separate it into four isosceles triangles
B). The diagonals of a rectangle are congruent
C). The diagonals of an isosceles trapezoid are congruent
D). The diagonals of a square are congruent
E). An equilateral triangle is also an isosceles triangle
F). all of the above are false
G). all of the above are true
All statements are true
Find the domain of f(x)=(sqrt(x^2-16))/(x^2-5x-50
(-infinity, -5) U (-5,-4] U [4,10)U(10,+infinity)
Which of the following are not one-to-one functions and why?
A). f(x) = x2-3
B). f(x) =x3
C). f(x) = x4
D).f(x) = x - 5
Parts A and C are not one-to-one functions since they both fail the horizontal line test
Write a function h(x)= (4 sqrt(x) +6)^2 such that it is the composition of 3 functions, f(x), g(x), and k(x). Write the 3 functions clearly and write the final function h(x).I do not know the order if you do not state it
f(x)=2x+6, g(x)=x^2, k(x)= 2 sqrt(x), h(x)=g[f(k(x))]
Given f(x) = (x3-x)/(2x4+x6) , classify the function as
A). odd
B). even
C). neither
Show all of your algebra and simplify completely
Replace x with (x)
we obtain [(-x)3-(-x)]/[2(-x)4+ (-x)6] which gives us (-x3+x)/(2x4+x6). Since the denominators are equal we can add the numerators and we get a sum of zero, therefore, the new function is - f(x). It is an odd function
<A and <B are corresponding angles cut by two parallel lines and <B and <C are corresponding angles cut by two parallel lines. If m<A=(z+32)0 , m<B = (5y+10)0,and m<C=x0. If <D and <C are same side interior angles cut by two parallel lines and m<D is 1100, find x ,y , z, m<A, m<B, and m<C.
x=10, y=12, z =38, <s A, B and C are all 700
Find the domain of f(x) = sqrt(-x)+2/(x+1)
(-infinity,-1)U(-1,0]
Compare and contrast a function with a one-to-one function (in words). Note: you may not simply state that they pass a particular test
Functions and one-to-one functions are both functions, however, no two ordered pairs can have the same input in a function, but in a one-to-one function, no two-ordered pairs can have the same output
Given f(x)=-5 sqrt(x), h(x)=-3x^2-3x-200, w(x)=-x+500
Given k(x)=f(w(h(f(25)))). Find k(x) Show the answers to all functions and then your final answer k(x)
f(25)=-25, h(-25)=-2000, w(-2000)=2500, f(2500)=50(-5), therefore, f(w(h(f(2500))))=-250
Fill in the blank with the correct answer
A). An odd function is symmetric about the _____
B). An even function is symmetric about the ___
C). A one-to-one function is symmetric about ___
D). Given f (1, 1) if the points(-1, -1) lie on the graph of f (x ,y) the it is symmetric about _____
A). the origin
B). the y-axis
C). the line y = x
D). the origin
In a geometry course, can we use the Angle-Angle-Angle postulate to prove two triangles are congruent? if not, explain why
No, because we violate the Triangle Sum Theorem
Given f(x) = -3-x and g(x) = -x3-3x2-x
find g[f(x)]. Simplify completely
g[f(x)] = x3+6x2+10x+3
given f(x) = x-3 and g(x)= 2 sqrt(x)
, if h(x)=f[g(x)], find h(x), h-1(x), and the domain and range of h-1(x)
h(x)=
h-1(x)=[(x+3)/2]2,
h-1(x) domain range
[-3, infinity] [0,infinity]
given f(x) =
2 sqrt(x) +8
and g(x) = 5x-6.
if h(x)= f[g(x)], find h(x), h-1(x), and state the domain and range of h-1(x).
h(x) = , h-1(x)= 1/5[(x-8)/2]2 +6
domain of h-1(x) = [8,+infinity)
range of h-1(x)= [6/5,+infinity)
Given f(x) = |x|, write a function g(x) which describes the transformation of f(x) to g(x):
Compress the graph horizontally by a factor of 1/2. Shift the graph 1/2 unit to the right. Reflect the graph across the x-axis, and shift the graph upward 4 units.
g(x)=-|2(x-1/2)|+4
Which of the following has a false converse statement
A). If <1 and <2 are vertical angles, then m<1 = m<2
B). If I live in Jersey City, then I live in New Jersey
C). if (a)(b) <0, then a < 0
D). If two angles of a triangle are congruent, then the sides opposite those angles are congruent
Parts B and C are false conditional statements