An infinite discontinuity of the given function can be drawn at x = %3D {(x): x+2 %3D 3x-6

Q: Draw the graph of f(x) and discuss its differentiability at x = 1

A: It is given that fx=x2x≤1xx>1. Recall the fact that formula for derivative of a function f at a…

Q: Where does the graph of the function x* +x - 6 cross the x-axis? O At x = -6 O At x = -3 and x - 2 O…

A: We use condition if any graph cuts or crosses X-axis then y coordinate becomes 0.

Q: if x -3 Step 3 of 3: Identify the correct graph of this piecewise-defined function.

A: To Draw : diagram

Q: True or false: The graph of the reciprocal function f(x) =1/x has a break and is composed of two…

A:

Q: Analyze the graph of f (x) = ln(x2 + 2x + 3).

A: The given function is f(x)=lnx2+2x+3

Q: Question 2 Find the intervals of concavity of the function g(x)= 3x4 – x3

A:

Q: Find the open intervals on which the function is increasing or decreasing.        y = x + 9/x

A: To find the critical points we solve dy/dx=0

Q: Find the open intervals on which the function is increasing or decreasing          g(x) = (x + 1)3

A: We first find g'(x)

Q: Find the open intervals on which the function is increasing or decreasing.

A: A function f(x) is increasing if for each x1<x2 we have fx1<fx2. Similarly a function f(x) is…

Q: The graph of f(x) = is (increasing/decreasing) over its domain.

A:

Q: 1. Let f(x) = -(x - 3)2 + 1. Find the vertex. Give the range of the function.

A:

Q: Compare the graphs of the functions. Y = In and Y, = Inx - In 2

A: Given: The functions given are  Y1=lnx2   &  Y2=ln x -ln 2

Q: 6) Sketch the graph of the following piecewise function. x 3 x – 4 h(x) = 7 x² – 1

A: Given ,  h(x) = x - 4 ; x < -2 Then ,  h(-3) = -3 - 4 = -7 h(-4) = -4 - 4 = -8 And  h(x) = 7 ; -2…

Q: Show that the production function f(x) = - () x³ + 10x² + 5x, –∞<x<∞ has both a concave and convex…

A: Given f(x)=-23x3+10x2+5x, -∞≤x≤∞ Consider the function f and its derivative f' can be differentiated…

Q: Find the value of k that makes the following function continuous. Graph the function. x2- k, if x…

A:

Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Asymptote is a line along which the function tends to infinity or minus infinity. Horizontal…

Q: find the horizontal asymptotes of the function by computing the limits at infinity.

A: Find the limits at infinity,

Q: The domain of the function fal= ln (6-5x-x²) is

A:

Q: what is the graph of the following function (2x+1)(x+2)/(x-1)(x-3)?  where are it's vertical and…

A: The objective is to draw the graph and find vertical and horizontal assymptote.

Q: Find f^-1 (x), if it exists, and graph both f(x) and f^-1 (x).  f(x)= 2x^3 -3

A: Topic  =Functions

Q: The graph of f(x) = is (increasing/decreasing) over its domain. 3 ()

A:

Q: Does y = e9-x* – 2 exist? What is the domain & range of the function if it does exist?

A:

Q: If g'(x) =-3x(x+2), then the graph of g(x) has a relative maximum at what value(s) of x?

A:

Q: Determine the intervals of concavity for the graph of f(x) =  lnx/x

A:

Q: 3. -2y = x + 4, 0 <x< 4

A: Given: The function is -2y=x+4. The interval for the function is 0&lt;x≤4

Q: 3. Graph the function well. 0 and create a table of values for this function as

A:

Q: Find the vertical and horizontal asymptotes of the function f (x) = x /(4 − x) .

A:

Q: By inspecting the graph of the function, find the absolute maximum and absolute minimum on the given…

A: From the given problem:   hx=x2-1x∈-4,5   Now differentiate the given function with respect to x and…

Q: 7. Graph the piecewise function for for -4<x <-3 - 3 < x <0 T<-4 -4x 13 f(x) = %3D x2-6x 7 for for 0…

A:

Q: 2. Given the graph of the function:

A: Given :    Reciprocal graph is given .

Q: The graph of a function defined for x 2 D is given. (a) Complete the graph for x<0 to make an even…

A: The given graph is,

Q: Find the slope of the graph of the function at the given point.                        f(x) = 27/x3…

A: Given: fx=27x3Point3,1

Q: Find the absolute maximum value of the function f(x) = 5(x - e

A:

Q: The graph f(x)- x² is transformed to create m(x) - f(bx)², where "b" is less than 1 but greater than…

A: Given function is                                                                         f(x)=x2…

Q: How many asymptotes does the function Ax) = x-1 (x+ 1) have?

A:

Q: 5) f(x) = ²-4 x-2 4 if x # 2 if x = 2 Is f(x) continuous at x=2? Sketch the graph of the function.

A: (5) Solution:- Function can be written as :- Continuity of x2-4x-2:x&lt;2  or   x&gt;2, &amp;  4  :…

Q: 5) The graph of the function f(x) = 4-x has an inflection point at

A: Given: fx=x4-x We know that for any function, inflection point are points where second derivative of…

Q: Use the graph of the greatest integer function y =⌊x⌋

A:

Q: Consider the following function. 4 if x - 3 Step 2 of 3: Identify the general shape and direction…

A:

Q: Find the points on the graph of the function that are closest to the given point. f(x) = x², (0, 2)

A: Given: f(x)=x2 ,        0,2

Q: Find the maximum and minimum limits of the function X-2 (x + 2)²

A: Explanation of the answer is as follows

Q: The graph of function f(x) = x – 9x² + 7x is concave upwards on (-0, c0) O (-∞, 3) O (3, 0) O None

A: Given function is  f(x)= x^3 - 9x^2 + 7x

Q: The intervals on which the function f(x) = x – 4x° + 4x2 + 6 is decreasing

A:

Q: The function f(x) graphed below has a jump discontinuity at 2 1 -1 1 2 4 -1 X- 4 only. O*- -1 only.…

A: Jump discontinuity is when left hand limit is not equal to right hand limit.

Q: 22) Assuming this function never crosses its horizontal asymptote, state the domain and range o…

A: Solve the function

Q: Find the intervals of concavity of the function g(x)=2x4+9x3

A:

Q: 18. When is the function, f (x)=: 4 -3x? -3+ below the horizontal asymptote? x-1 5-4x-x2

A: It is given that the function fx=4x-1-3+-3x25-4x-x2. 5-4x-x2=5-5x+x-x2               =51-x+x1-x…

Q: Find the asymptotes of the function f(x)=x3 / x2+1.

A: Since the degree of numerator (3) is greater than the degree of denominator (2), therefore there is…

Q: Find the open intervals on which the function is increasing or decreasing.        h(x) = 12x − x3

A: Given function - h(x) = 12x-x3let's find the critical point of the function h(x) , by h'(x) =…

Q: Describe the behavior of the function p around its vertical asymptote at x=-9. p(x)=x squared +20x…

A: Given the function p(x)=x2+20x+100x+9