49–50 - Finding Piecewise Defined Functions A graph of a piecewise defined function is given. Find a formula for the func- tion in the indicated form. if x < -2 if -2 2 if x< -1 if -1 2

Q: 0 and f" (x) < 0 for all x 50. Suppose f(3) = 2, f'(3) and f'(x) 2 a. Sketch a possible graph for f…

A: We can conclude from f(3) = 2 that the value of f(x) at x = 3 is 2.So we got one point on the curve…

Q: x2 - 7x + 10 Let f(x) x2 -8x + 12 Find: 1) Domain (in interval notation) 2) Y-intercept(s) at the…

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Q: #55

A: 55.The given function,y=3-x1+x21-x4

Q: Given f(x) = 2(2x + 1)(x 1)? find the following." (a) The domain of f. (b) Critical numbers. (c)…

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Q: The graph of a function f is shown. (The dashed lines indicate horizontal asymptotes.) y4 1- Find…

A: We have to draw graph of y=|f(x)| from graph of y=f(x)

Q: 2. Graph the function. Be sure to label all the asymptotes. List the domain and the r- and…

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Q: Consider the function in the graph to the right. The function has a local maximum of at x = The…

A: Local maximum is defined as that point on the curve where the function has the highest value in its…

Q: Determine all of the relative extreme values of the function f (x) = x* - 8x2 %3D O The relative…

A: topic- relative extremes of the  function

Q: 8 11. For the function f (x) = 1 +2- x2 a. Find the vertical and horizontal asymptote(s) b. Find the…

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Q: 9. Find an equation for a function f(x) that satisfies the following characteristics. • f(x) is CTS…

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Q: If f(x) is a function with f'(4) = 0 and f"(4) = 6, then which one of the following must be true?…

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Q: 1. Use the function g(x) a. Use a calculator to graph g(x). Make sure you have a window that is…

A: The given function,       gx=2x2-4xx2-9

Q: (i) Find the largest integer k such that the function f(x) =x² +4x+3 with (restricted) domain x<k,…

A: f(x)= x2+4x+3a)x≤k, is a one-to-one function.Let x,k∈Rthenf(x)=f(k)x2+4x+3=k2+4k+3⇒x=k for all…

Q: 2 Consider the function f(x) = x+61 3. (a) Find the domain of f(x). Note: Use the letter U for…

A: "since you have posted a question with multiple subparts , we will solve first three subparts for…

Q: The graph of a function defined for x20is given. y (2) Complete the graph forx< 0 to make an even…

A: There graph of an even function is symmetric about y axis.

Q: 6x Let f (x) = 1+ 3x2 Find the requested information for the function f and its graph. When…

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Q: 37-5 on the axes below. You must plot the asymptote Graph the function f(x) = and any two points…

A: We have given  function fx=3x-5 We can see here when x→-∞ then, limx→-∞fx=limx→-∞3x-5=0 Therefore,…

Q: Which, if any, of the following statements is true about the function f(x) = 1 – 2x – 3x2 Choose all…

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Q: e-In a For sketching the function y = 42 determine the following " x-intercept y-intercept vertical…

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Q: 2x + 13 h(x) x - 4 x2 – x - 12 (a) At what x-values is the function h(r) discontinuous? For each…

A: Rational functions are discontinuous for the values of x, where they are not defined. Note that…

Q: 3. Find a function y = f (x) which has only one horizontal asymptote and exactly 2021 vertical…

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Q: 6. Given f (x) = (x – 2)² (x + 3) a) Find the interval(s) where the function is increasing and the…

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Q: 15.) Given 1 (x) = 2 + 2x – x : (a) Find the intervals on which f is increasing of decreasing. (b)…

A: Part (a):   Put the derivative of the function equal to zero and find the region positive and…

Q: 6x +1 The function f(x) 6x +7 is increasing on the interval and is decreasing on the interval The…

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Q: 3. function. g(x) = -f(x +3) – 1 when f(x) = %3D 8(x): x-intercepts: y-intercepts: vertical…

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Q: 4. Consider the function f(x) and its derivatives below: f(x)=2x²-11 Horizontal asymptote(s) f'(x)=…

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Q: 1. Given f(x) = x^2 - 1/x (a) Find the domain and x-intercepts. (b) Find all asymptotes. (c)…

A: fx=x2-1x=x3-1x To find The domain and x-intercepts Asymptotes Intervals on which function is…

Q: Find the transition points. -x)1/3 f(x) = x(17 –) (Use symbolic notation and fractions where needed.…

A: To solve the following problem of finding the transition point.

Q: 1. The graph of f "(x) is continuous and decreasing with an x-intercept at x = -3. Which of the…

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Q: 1. The graph of f '(x) is continuous and increasing with an x-intercept at x = 4. Which of the…

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Q: a) Find all values of x where the function is discontinuous, and (b) graph the given function f(x) =…

A: Here, the given function is: f(x)=2x+2            if x≤0x2-2x+2   if x&gt;0

Q: Given the functions: f(x) = 8 / (x2 + 4) a. List the vertical and horizontal asymptote(s). b. Find…

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Q: 1 + k with a vertical asymptote of x = h Write a function of the form f(x) 10 and a horizontal…

A: The given function is fx=1x-h+k with vertical asymptote of x=-10 and a horizontal asymptote of…

Q: The graph of the function f(x) is given. (a) give the graph of f(-x). Clearly identify the new…

A: topic- transformation of a function

Q: Creat a graph of a function f(x) with the following characterisitics. If possible, please do this on…

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Q: Sketch the graph of a function having the following properties: 1) The domain is all real numbers…

A: Given, 1) The domain is all real numbers except x = 1. 2) It has an x-intercept at (−1, 0) and no…

Q: 8. Describe the features of the graph of f(z) = . O The oraph of this function has a hole at (0,0).…

A: The given function is:f(x)=x+4x-1

Q: 1. Consider the function g(x) = . (d) Find the intervals where g is increasing and decreasing. Give…

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Q: 31-4 A piecewise function f(x) is defined by f(x)=x²+3x+4 x² -7x+12 Part A: Graph the piecewise…

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Q: 2x2 + x - 6 Let f(x) 2x2 + 5x + 3 This function has: 1) A y intercept at the point Be sure to put…

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Q: 12 3x with f' (r) - Let f(x): 18x 24 - - (х — 3)2 18(2x 1) and (x- 3)3 -- f" (x) - (x-3)4 a. Find…

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Q: A function f(x) = x +b has vertical asymptotes at x=-2 and x=2. Given f'(x)= %3D Find: i) The values…

A: The function f(x)=x2+bx2-a has vertical asymptotes x=-2 and x=2.f'(x)=-12x(x2-a)2

Q: 5. Find the requested information for the function: f(x)=- 3x -8x-3 x²-2x-3 Domain: Vertical…

A: We have to find x intercept and y intercept and horizontal asymptote.     According to our…

Q: 5 – 3x For the function h(x): find h'(x), construct a sign-chart of h'(x), and then fill in answers…

A: h'(x)=5-3xx2' =--3x+10x3 We know that for h to be increasing we must have h'(x)&gt;0 and similarly…

Q: (x- 4)2 The local extrema of f(x) = occur at which of the following x-values? O local minimum at…

A: f(x) = x-42xdiff. w. r. to xf'(x) = x×ddxx-42 - (x-4)2ddx(x)x2         = x.2(x-4) - (x-4)2×1x2…

Q: 12 can be obtained from the graph of y = Explain how the graph of the function f(x) = Then graph f…

A: We will find the domain ,range , graph and the interval over which the function is decreasing as…

Q: 5 – 3x 2. For the function h(x) = find h'(x), construct a sign-chart of h' (x), and then fill in…

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Q: x+1 4. Sketch the graph of f (x) = x2-4x-5 by using 9. 5 4- (1) The domain: 3- (2) The vertical…

A: Domain of a function y=f(x) is a set of values of x for which this function is defined. x=a is said…

Q: 1. The graph of f '(x) is continuous and increasing with an x-intercept at x = 4. Which of the…

A: Let's solve.

Q: 2. Graph p(x). Using the properties of reciprocal functions, complete the table and graph q(x) = 76…

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: