For each function in Exercises 1-6, state: a) the maximum number of real zeros that the function can have; b) the maximum number of x-intercepts that the graph of the function can have; and c) the maximum number of turning points that the graph of the function can have.

Q: In Exercises 117-118, find the coefficients that must be placed in each shaded area so that the…

A: Given: y=12 x-intercept=-2 y-intercept=4 y-intercept =-6  slope =12 To form the line equation

Q: Sketch a graph of an odd function f and state how f1x2 and f1-x2 are related

A:

Q: Exercises 71-98: Sketch a graph of f. 72. f (x) = –2x²

A:

Q: Sketch the graph of g(x) = (3 + 2x)/(1 + x) and state its domain.

A: given,       g(x) = (3 + 2x)/(1 + x)

Q: Sketch a graph of any cubic polynomial function thathas a negative leading coefficient and one…

A: suppose, we have a polynomial function, y=-2x-2x2+1

Q: Sketch a possible graph of a quadratic function, whose discriminant is 0 and its graph opens…

A:

Q: Sketch a graph of f(x) = |2 - 1- 2 1.

A: Given Data: Function: fx=12x-1-2 ......1 Substitute different values of x to obtain values of f(x).…

Q: What is the integer floor function?

A:

Q: For each function in Exercises 1–6, state: a) the maximum number of real zeros that the function can…

A: Here, the given function is f(x)=x10-2x5+4x-2. (a) The maximum number of zeroes for a polynomial is…

Q: give the domain and range of the quadratic function whose graph is described. Maximum = - 7 at x =…

A:

Q: For each graph in Exercises 56-66, find a function whose graph looks like the one shown. When you…

A: To write: The equation of the function represented by the given graph. To sketch: The graph using…

Q: complete the square of each quadratic expression. Then graph each function using the technique of…

A: Complete the square using the identity a+b2=a2+2ab+b2.

Q: Determine and graph the domain of the function: f(x,y) = ev- + In(5x² + 7vZy² – v2) |

A:

Q: Which function has a domain of all real numbers and an x-intercept of -3?

A:

Q: Sketch the graph of f.

A: f(x)=8-x32x2

Q: Write the domain of the given functions in interval notation:

A: here we have to find the domain of the given functions.

Q: Sketch a graph of an even function f and state how f1x2 and f1-x2 are related.

A: If f(x) is even function then  f(-x)=f(x) Graph of even function is symmetric about y-axis. Function…

Q: Is the point (1, -2) on the graph of the function k(x) = x2 + (2>x)?

A: Given, k(x) = x2 + (2/x) To check Is the point (1, -2) on the graph of the function

Q: a. List each real zero and its multiplicity. b. Determine whether the graph crosses or touches the…

A: Given that: The equation h(x) = (x - 5)2(x + 4)3 .

Q: Let f(x)=-2x'-10x+12 (a) Express f in standard form (b)Find the vertex (c)Determine if the vertex is…

A:

Q: Sketch a graph of the piecewise defined function.

A: f(x)=1-xif x<-25if x≥-2

Q: Sketch a graph of f(x) = .5 - 2 2

A: f(x)=0.5|x-2|-2

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A: solution is given below:

Q: Draw Graphs of three polynomial functions?

A: Let us take three polynomial 1. x3+2x2+3x+22. x2+4x+73. x4+5x2+10

Q: Sketch the graph of each funetion. (-x-1, x<0 8) f(x) = (-4,

A:

Q: sketch the graph of each quadratic function and compare it with the graph of y=x square. f(x) =x2…

A:

Q: The set of all images of the elements in the domain of a function is called the…

A: We know that the set of all images of the elements in the domain of a function is called the Range

Q: Plots the graph of the function f(x) - 2x2 - 4x + 1, sets its domain, range, the coordinates of its…

A: Here we construct table for the f(x).

Q: Sketch the graph of f(x)=x² /x²-1

A: Graph

Q: 6+ Write the domain of the function using interval notation.

A: Domain:- All possible value of x

Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…

A:

Q: Every quadratic function has a U-shape graph called a Ex:

A:

Q: a quadratic relation has zeros at -1 and 3, and a y-intercept of -18. Determine the equation of the…

A: We want quadratic  in vertex form. In the vertex form quadratic  equation  is of type y = a(x-h)2 +…

Q: Find the domain and express it in interval notation

A: Domain:                      Domain is the set of input values where for which the function is…

Q: Show an example illustrating the theorem

A:

Q: Determine the quadratic function whose graph is given below.

A: Given, Vertex (h,k) is (-2,10) Point (x,y) is (0,-6)

Q: Give an example of a function whose domain is the set ofreal numbers and that is neither increasing…

A: A function that is not increasing or f'(x)&gt;0 or decreasing f'(x)&lt;0 and for such a function to…

Q: Sketch the graph of f(x)= 1/3x-x-3x+4 showing all the points of inflection, local max. and local…

A: It is defined that the inflection points are those points at which the rate of change of slope…

Q: Sketch the graph of the quadratic function by finding the vertex, intercepts, and determining if the…

A:

Q: Find a formula for the polynomial of least degree that is graphed below.

A: Given: To Find: The formula for the least degree of the above graph.

Q: Exercises 21-34: Use the graph of the quadratic function f to write its formula as _ƒ (x) = a (x −…

A: By using the graph of the quadratic function f to write its formula as fx=ax-h2+k

Q: Use the guidelines of the section to make a complete graph of ƒ.

A: Given function f(x) - f(x) = 3xx2-1Let's first check where the function is defined, for the function…

Q: Find a function whose domain is the set of all integers and whose target is the set of all positive…

A: Step:-1 Set of integers = ℤ=........-3, -2, -1, 0, 1, 2, 3,........, set of positive integers= ℕ=1,…

Q: In Exercises 13-14, find the domain of each function. 13. f(x) 3 (х +2)(х — 2) 14. g(x) (х + 2)(х —…

A: 13. f(x)=(x+2)(x-2) 14. g(x)=1(x+2)(x-2)

Q: Determine the quadratic function f whose graph is given.

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Q: Sketch the graph of f(x) = x4 – 3x3 + 3x² + 1 containing intercepts, inflection points, local max,…

A:

Q: sketch the graph of f(x) = 2x and label two-point.

A:

Q: Which quadratic graph correctly shows f(x) = 4x2 + 3x - 1 -2

A:

Addition Rule of Probability

It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.

Expected Value

When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).

Probability Distributions

Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.

Basic Probability

The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.