2. Consider the function below. x + 2, f(x) = {1 (7x +6, 2

Q: 4. Consider the function f(x) = |x + 1|whose graph is shown below. 4. a. Is the function…

A:

Q: Consider the function f(x) = x-2 x²-4

A: The given function is f(x)=x-2x2-4. To Examine: Continuity of f at -2 and 2.

Q: 2. Sketch the graph of the function below using the maximum and minimum function value. g(x) = 2 –…

A:

Q: Find the points on the graph of the function that are closest to the given po f(x) = x2 – 9, (0, -5)…

A: Put first derivative of distance =0

Q: 3. Find the domain and the range of the functions below. a) f (x) |x | b) g (x)

A: Given a) f(x)=19-xb) g(x)=|x|x

Q: 3) Without a graph, how can one show differentiability of a function at a point? 4) Where is the…

A:

Q: What happens to the function f(x) = (x – 1)² +1 when it becomes f'(x) = ((x- 1)² + 1)? O It is…

A: topic - transformation

Q: 5. 5) For the function below, give all the important information about its graph. f(x) = 8 -csc(14x…

A:

Q: a) What is the height of the function, f(x)? Give your answer as a reduced fraction.

A:

Q: Q2\\ Find the value of (a) that make the function below continuous at x 2: (a*x-2a x22 fx) = 12 x<2

A: Definition used-                     Continuity of function -                     A…

Q: 4. Given the graph of f(x) below, sketch the graph of f'(x) and explain how you arrived at your…

A: The graph is drawn by free hand.

Q: 8. f(x) = %3D Use the drop-down menu below to make a true statement based on the function shown…

A: Given, f(x)=8/(x-1)-------(1) Now replacing x with 2 in (1), we get f(2) = 8/(2-1) f(2)= 8/1 So,…

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

A:

Q: Q.2 Apply vertical line test to show that the graph of the function 4 =1 does not 9. represent the…

A: To Determine: Apy vertical line test to show that the graph of the function does not represent the…

Q: 11) Find the point of inflection of the graph of the function. f(x) = xVx – 27 %3D

A:

Q: Hi, The question is as follows Evaluate the function for values of x that approach 1 from the left…

A: We are getting 0 in denominator if we use the limit x-&gt; 1^- or x-&gt; 1^+. So lets check it using…

Q: Sx² + 2 , lx² – xk – 3 , x 5 10. Find the value of K that makes the function f(x) = Continuous at x…

A: We have to find k

Q: 3 3 For the functions f(x) and g(x) ==+4, find f(g(x)) and g(f(x)), %3! х — 4

A:

Q: Find the point of diminishing returns for the function, where R is the revenue (in thousands of…

A: Solution

Q: 4. What is the domain and range of the parent function, and what is the domain and range of f (x)?…

A:

Q: 2. f(x) = 3[ x]

A:

Q: Q4: Evaluate the function at the given values f(x) = v20 – x² when x = - 4

A:

Q: 2a5 Given that f(x) = and values h(-1) =-3. h'(-1) = 7, find f(-1) AND f'(-1). h(x) %3D Show your…

A: f(x)=2x5h(x), and values h(-1)=-3, h'(-1)=7

Q: Q2// Sketch the graph of the function defined by the formula 0, xS-1 f(x) ={V1-x2,-1<x<1 x , x21

A: We have to sketch using the function in the suitable intervals.

Q: 3. Which of the following statements is correct for the function A(I)=-x²+9x, where A(I) is the area…

A:

Q: Find the absolute extrema of the function on the closed interval. 3 f(x) = x³ – , [-1,2]

A:

Q: (2) For the function f(x) = -x² – 24x +19

A:

Q: What is the average rate of change between x = 4 and x = 7 for the function g defined below? 3 g(x)…

A:

Q: 35. Estimate any extrema of the function given by g(x) = x3 – x3.

A: The extrema of a function are the maximum and minimum values of the function. To find the critical…

Q: (2) (a) Find the points of inflection and discuss the concavity of the graph of the function f(x)…

A:

Q: 8. A student writes the following for the function f(x) = - Br+8 " The domain of f(x) is (-2, -4) U…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. Determine if the function is even or odd g(x) = x³ +x, f(t) = 1 + cost

A: Given function are gx=x3+x and ft=1+cost. To determine whether function is even or odd. Solution: A…

Q: 2. Use the graphs of y=f(x) and y= g(x) to sketch the graph of y=h(x). Hint: Estimate the function…

A: answer is in next step.

Q: Find the points of inflection and discuss the concavity of the graph of the function f(x)= x +…

A:

Q: What is the range of the attached function?? Is it f(x)&lt;=3/4 or f(x)&gt;=3/4

A: Given the funciton f(x)

Q: What happens to the function f (x) = (x – 1)² + 1 when it becomes f'(x) = ((x – 1)² + 1)? O It is…

A: We have to find out the rule

Q: Q4:- Sketch the following functions showing the detailed steps in different graphs: f) f(x) = 1-x2

A: fx=11-x2

Q: 1. Consider the function f(x)= x5- 5x4+5x3 a. When is ? increasing? When is it decreasing? b. When…

A: Let us first evaluate the derivatives of the given function as shown below:…

Q: 13. Use the idea of transfr-mation to sketch the function y = -2f(x+2) + 3 if the graph of y = f(x)…

A: Given: The graph of y=f(x) is

Q: 9. Sketch the graph and determine the domain and range -x', x 2

A:

Q: 9. Sketch the graph of the function y = Va + 2 and determine the domain and range.

A: We have to draw the graph

Q: For sketching the function y = 3-e² 2e² determine the following

A: Note: As you asked only for subparts 4, 5, 6, and 7 so, I answered here only that.

Q: 25 Given the function f(x) = x°+ x° + x*, find all x-values where f has an inflection point.

A:

Q: 3x Consider the function f(x) = x2 +4x-5 For what value(s) of x is the function undefined?

A: The given function,   fx=3xx2+4x-5

Q: 2. Find the domain of the following function. State your answer in interval notation. 2х- 1 + vx 2.…

A: Given function:

Q: 15) What is the domain of the function f(x) = E (r + 5)"? %3D

A: Domain is same as convergence interval

Q: True or false: The graph of f(x) = (x + 5)2 + 3 has its vertex at (5, 3)._______

A: For  f(x)=a(x-h)2+k, vertex is (h,k)

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: 1. Given the function f(x) = 20 √7-x find f (-9). "

A: The given function is: fx=207-x    ...1

Q: Find the slope of the secant line between x = -3 and x = -1 on the graph of the function f(x) = 3x²…

A: Given function, fx=3x2-x+3We have to find the slope of the secant line x=-3 and x=-1 on the graph of…

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: