Use the following function and its graph to answer (a) through (d) below. 6-x. x<4 Let f(x) = 3x +1, x>4.

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: Find the value of k that makes the function continuous. Justify your answer. 2x – 1, x 2

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Q: Given the function h (x) = -v2 – x, what is h (x)?

A:

Q: Consider the following function: -4x – 7 f(x) : x +5 Step 1 of 2: At what x-value is the function…

A: The given function is fx=-4x-7x+5. Rational functions are continuous everywhere except when the…

Q: Use the given graph of the function to find the x-values for which f is not differentiable.

A: Using graph to find the x-values where function is not differentiable

Q: Determine the range of the following functions. Express your answers using interval notation y =…

A: The graph of y=3x2, -2≤x≤2 is shown below:

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A:

Q: Use the graph of the given function f(x) to find x such that f(x) = - 3. 2- ->

A: f(x) implies y in a cartesian plane so the value of y is the value of f(x)

Q: Consider the function below. List the answers. x2 – 7x + 10 | f(æ) = а? — 4х — 5 - - For what real…

A: Recall: Removable discontinuity is a point at which a graph is not connected but can be made…

Q: For Exercise, use a graphing utility to graph the piecewise-defined function. S2.5x + 2 f(x) = l² -…

A: We will graph the piecewise function as two separate functions:

Q: is the interval of decrease for the following function? f(z) =-|z – 2| +3

A: Topic = Functions

Q: Find the value of k that will make the function f(x) continuous. -x2+8, if x+ 3 f (x) =, k, if x=3

A: topic - limits and continuity

Q: Consider the function. f(x) = 9x2 – 2, x = 1 to x = 2 Find the area (in square units) under the…

A: As we know that the area under the curve f(x) is : Area=∫abf(x)dx

Q: Find the points on the graph of the function that are closest to the given poir f(x) = x2 - 8, (0,…

A: Solution

Q: Find the value of the constant & that makes the following function continuous on (-o, o). | 2x – 6…

A: fx=2x-6     if  x≤6-3x+b  if  x&gt;6 Since the function is a polynomial function for all x&lt;6…

Q: What type of discontinuity does the function f(x)=xsecx have?

A:

Q: Consider the following function: 6x + 9 f(x) = x+ 8 Step 1 of 2: At what x-value is the function…

A:

Q: What is the value "L", if exists, when a variable "x" in f(x) approaches a certain number "d" in the…

A: Given: A function fx is given. To Find: What is the value "L", if exists, when a variable "x" in…

Q: Find the value of the constant bl that makes the following function continuous on (-00, 00). if x 6…

A: The given function is fx=2x-6if x≤6-3x+bif x&gt;6. it is given that, the given function is…

Q: Find a formula for a function that f(x) =

A:

Q: Apply the definition to differentiate the following functions: 1- y = ₁

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Q: Find the domain and sketch the graph of the function.

A: fx=x+2    if x≤-1x2        if x&gt;-1 The domain of given function is the set of all real numbers.

Q: en the function f(x)= – (x+4)3, which of the following statement talks about its relative and…

A:

Q: The function f(æ) can be approximated by L(x) = 3 – 2(x – 4), near x = 4. What is the value of f'…

A: topic -linear approximation

Q: X- e.

A:

Q: 3. For the following piecewise function, sketch a graph, determine whether the function is…

A:

Q: Explain why the function is discontinuous at x = 1. f(x) = (3 Зх for x 1

A: We have to find the left and right-hand limit of f(x) at x=1 So the right and left hand limits are…

Q: 9) Differentiate the following function. Simplify your answer as much as possible. Show all steps y…

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Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: Graph the function. f(x) =. * for x<0 x+3, for x20 Choose the correct graph below. OA. OB. OC. OD.

A: Given, fx= 18x      for  x &lt;0x+3   for   x ≥ 0  We have to graph the function.

Q: Which of the following describes a true relationship between the functions f(x) = (x- 3)2 +2 and…

A: We have the following graph

Q: The graph of  f(x)  and a line tangent to the curve at  x = 4  are shown. If  g(x) = sqrt(f(x))…

A: In the question it is asked to calculate the value of g'(4) for g(x)=f(x). for the graph given…

Q: For what values of x is the function f(x) = x* - 2x? strictly increasing?

A: fx=x4-2x2 Differentiating with respect to x, we get f'x=4x3-22x=4x3-4x

Q: X+1 5) Is the function given by f(x) x2 - 8x + 15 continuous at x = 3? Why or why not?

A: f(x)=x+1x2-8x+15

Q: For each statement, explain why it must be true, or use an example to show that it can be false. •…

A:

Q: How much revenue does the company get from a customer who uses exactly 30 therms of gas in a month?…

A:

Q: 4. If f(x) = ax' +bx', determine a and b so that the graph of f will have a point of inflection at…

A: we need to determine the values of a and b.

Q: Consider the function f(x)=/25-x² . Is L(x) an overestimation or an underestimation of ƒ(x) near…

A: Differentiate the function fx=25-x2 with respect to x, to find f'(x) and f''(x). Calculate f(3) and…

Q: Make a graph of the functionƒ(x) , for x ≥ 1. Be sure to include all of the evidenceyou used to…

A: Given:  The function fx=∫1xdtt for x≥1, To sketch: The graph of fx for x≥1,

Q: Use the graph of f(x) = [[x]] to graph the indicated function. y = [[2x]]

A: Given function is: y=[[2x]] It is greatest integer function. Given basic function is: fx=[[x]]

Q: A function has a zero at X = 8, indicating what?

A: Given, A function has a zero at X=8

Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: h) f(x) = |Inx|

A: Sketch the following function showing in the given expression.  f(x) = 1/|lnx|

Q: Use the given graph of the function to find the x-values for which f is discontinuous. Answer…

A: Graph of function is

Q: Use the given graph of the function to find the x-values for which f is differentiable. not 1,0

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Q: (c) Explain why the following function is discontinuous at x = 1. (x² f (x) = if x + 1 х2 — 1 - 1 if…

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Q: Consider the following functions. f(x) = x and g(x) = x2 – 10 Step 4 of 4; Find -(-2).

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Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…

Q: Given the function f(x) = - (x+4)3, which of the following statement talks about its relative and…

A:

Q: . Find f(x), knowing that f (x)=10-0.5x +3x and that the graph of f(x) passes through the point…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.