9. Sketch the graph and determine the domain and range -x', x<-2 (d) f(x) =-, -2 2

Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

A: Consider the function

Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: 30. Consider the function defined by 0ifx 1 Sketch this graph and find all points where the graph is…

A:

Q: If a continuous, differentiable function f is equal to 2 at x = 3 and at x = 5, what can you say…

A: Given f(x) is continuous and differentiable and f(3) = f(s) = 2Concept Roll's Theorem If f(x) is…

Q: 2) What is the Domain and Range of y =Tanx Function Domain: Range:

A:

Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: Use a graph below of f(x) = 3e-5z to estimate the x-values of any critical points and inflection…

A:

Q: 50. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Given: fx=3x-2 Concept Used: Linear function is continuous everywhere.

Q: Find the absolute extrema for f (x) = -x² – 1 over [-2,2] .

A: Please refer the attached image for complete solution.

Q: Find the length of the curve of the graph of the indicated function. y = In(sen x), between points…

A:

Q: F(X)

A: y = f(x) is continuous at x = a  only if following properties are satisfy : (1)  f(a) exists . (2)…

Q: If the limit of f(x) is 1 as x approaches 1 and the limit of g(x) is infinity as x approaches 1,…

A: we have to find the limit of the following

Q: 2. Is the function given by f(x) = 3x - 2 continuous at x = 5? Why or why not?

A: Is the function given by f(x) = 3x - 2 continuous at x = 5?

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: Let X2=mY , where 'm' belongs to set of integers. And here we have taken a parabolic path .

Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

A:

Q: Find f'(x). 6. f(x) = 4x + 7x f'(x) = Compare the graphs of f and f' and use them to explain why…

A:

Q: given f(x)=x^2-2x use the limit defintion of derivative if f'(-2)

A:

Q: Find the instantaneous rate of change of each function at the given x-value. Use the form lim…

A: a) Given that…

Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We know that Critical points are points where the function is defined and its derivative is zero or…

Q: 15. If f(x) = x2 - 6x - 9, find f(x) by using the formula/limit definition of derivative.

A: Given: fx=x2-6x-9 we know that derivative for any given functionfx by using limit definition is…

Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: The tangent line to the graph of a function f at the point x =2 has x-intercept 10/3 and y-intercept…

A: Given query is to find f(2) and f'(2)

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

A:

Q: 6. Find the length of the curve given by the graph of the function f(x) = x/x, for x in [1,4].…

A:

Q: What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x &lt; 1?…

A: Use the graphical approach to determine the maximum and minimum values of the function y = | x | on…

Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

A:

Q: Suppose that the function y=f(x) is increasing on the interval (-1,5). Over what interval is the…

A: The x-5 is offsetting the input of x. The beginning of the function increase is at x-5=-1 and the…

Q: 7. Give two reasons why a function might not be differentiable at a particular value of x.

A: topic -derivative

Q: Find the critical numbers of the function f(x) = 14x + |x|. In the answer boxes below, enter the…

A: Given: f(x)=14x3+|x| Definition: Critical points are the points where the derivative of function is…

Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

A:

Q: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

A:

Q: Find the value k that makes the function continuous. kx f (x) = x > 9 - -7x – 7, x < 9

A:

Q: Find the absolute extrema for the function over the specified domain. y = x2 5 over [ – 1, 2] -

A:

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: What is the lower limit and upper limit bounded by the curves y 9 - r2 and the line y = x + 7 ? -2…

A:

Q: 3. Is the function given by g(x) = x² x = 4? Why or why not? 3x continuous at

A:

Q: A function y = f(x) is decreasing on the interval [0, 5]. What conclusions can you draw about the…

A: A function is increasing, if when x increases, the value of y also increases.          Since the…

Q: Determine the interval(s) on which f(x)=square root(x/x-4) is continuous.

A: Given query is to find the interval where function is continuous.

Q: Prove without graphing, that the graph of the function has at least two x-intercepts in the…

A:

Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

A:

Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)

Q: 6. Is the function given by F(x) = at x = 4? Why or why not? 1 x² - 7x + 10 continuous

A:

Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.