Q2: (a) Graph the following functions by using vertical and horizontal shifts: (i) y = (x + 3)2 - 2 (ii) y = (x – 2)2 + 2 (b) Determine the domains and range of this function: y = v1- x2

Q: Starting with the graph of f(x) = 8², write the equation of the graph that results when: (a) f(x) is…

A:

Q: what is the decreasing interval for the following function: y = -1/4x-5

A: The given function is: y=-14x-5 The function f(x) decreases when f'(x) < 0.

Q: Q.4 Find the horizontal and vertical asymptotes of the function Vr --3x-10 y% = x --10x + 25

A: Consider the function: y=x4+3x2-10x2+10x+25. Find the horizontal and vertical asymptotes.   A…

Q: Starting with the graph of f(æ) = 2", write the equation of the graph that results from a.…

A: Given: f(x) = 2x

Q: Starting with the graph of f(x) = 4°, write the equation of the graph that results from (a) shifting…

A: Given: f(x) = 4x

Q: find the domain and Range for the functions FCx) from the graph below! y, 3 -2 • 3 1

A:

Q: Starting with the graph of f(x)=5^x, write the equation of the graph that results from a. shifting…

A: Transformation of graph

Q: Use the graph of y = f(x) to sketch the graph of f'(æ). 10+ 7+ 6+ 5- 4+ 3+ 2-

A: In this question we will use basic of calculus i.e differentiation and sketching of curve. We will…

Q: Sketch the graph of y = f(2x) and y = f(x), where f(x) = \x| +1

A: The figure below shows the graph of y=f(2x)=2|x| + 1.

Q: Q3) Let f(x) = x², draw the graph of (x + 2)², what is type of this shifting and what is the value…

A:

Q: Starting with the graph of f(x) = 7* , write the equation of the graph that results from (a)…

A: Given that: f(x)=7x

Q: Starting with the graph of f(x) = 4*, write the equation of the graph that results from (a) shifting…

A: solution:-

Q: Sketch the graph of the function f (x, y) = 10 – 4x – 5y.

A:

Q: Using the first and second derivatives, sketch a graph for y=3x^3-4x^2-2.

A: Solution: The objective is to graph the given equation y=f(x)=3x3-4x2-2

Q: Use the graph of y = f(x) below to graph the function y = –3f(x – 2) 5- 4- 3 2- y = f(x) 1- -6 -5 4…

A: topic - functions

Q: 6. For the function, y=x² - 4x - 5, complete the table then graph. -2 -1 1 4 2 10 -8 6 -4 -2 2468 10…

A: the equation given to us is  y=x2-4x-5

Q: Starting with the graph of f(x) = 6ª, write the equation of the graph that results when: (a) f(x) is…

A:

Q: Starting with the graph of f(x) : 7", write the equation of the graph that results from (a) shifting…

A: graph of  f(x)=7x

Q: Starting with the graph of f(x) = 9ª, write the equation of the graph that results when: %3D (a)…

A: Write the equation of shifting

Q: Q4, Using Vertical Shifts and Horizontal shirts in Graph of Runctions: O y = (x+2)-3 © y = Cx=2)+3

A:

Q: Starting with the graph of f(x) = 2", write the equation of the graph that results from a. shifting…

A: NOTE: Refresh your page if you can't see any equations. . the base function is the graph of the  is…

Q: The graph of y =f(x+3)  is obtained from the graphof y = f(x) by shifting_________ 3 units.

A: Given, y =f(x+3)

Q: Starting with the graph of f(x) = 9", write the equation of the graph that results from a. shifting…

A: In case of upward or downward shifting magnitude of function f(x) increase or decrease respectoiely…

Q: Starting with the graph of f(x) = 2, write the equation of the graph that results from (a) shifting…

A: Given graph equation , f(x)=2x (a) shifting f(x) 1 units upward, y= f(x)+1 =2x+1. (b) shifting f(x)…

Q: Find the z- and y-intercepts of the graph of the function f (z) =-3|z+5+9. %3D Enter your answers as…

A:

Q: Starting with the graph of f(x)=4xf(x)=4x, write the equation of the graph that results from A.)…

A: (i) Consider the given function as fx=4x. a) A function y=fx when reflected about the x-axis becomes…

Q: Starting with the graph of f(x) = 3", write the equation of the graph that results from %3D a.…

A: Given query is to find the equation after performing indicated transformation.

Q: Sketch the graph of y = f(2x) and y = f(½x), where f(x) = lxl + 1

A: It is given that, f(x)=|x|+1   and if y=f(2x), then the function will be, y=f(2x)⇒y=|2x|+1⇒y=2|x|+1…

Q: Starting with the graph of f(x) = 9ª, write the equation of the graph that results from a.…

A: Since you have asked multiple question As per our policy, we will solve the first question for…

Q: Q3:1) Is y = -V1 – x2 a function? 2) Graph the function f(x) %3D x< 0

A:

Q: Use the graph of y = f(x) given above to find: a) f(-1) = b) f(-3) =

A: We have to find the following values using the given graph.

Q: Use the graph of y = f(x) to sketch the graph of f'(x). 10+

A: The given graph is:

Q: 2 Q5 / Sketch the graph of function y = =+ 3x

A: Given function is y=2x+3x Domain : ℝ-0 where ℝ denotes the set of real numbers  Range : (-∞,…

Q: Use the graph to determine the function's domain an y 4 3 2 -5 -4 -3 -2 -1 3 -1- -2 -3ト 2.

A: Given query is to find the domain and range of the graph.

Q: V3 1, a -1

A:

Q: 6. Determine the x-intercept(s) and the y-intercept of the function f: R R, f(r) = 3x-2 and sketch…

A: See the attachment

Q: Starting with the graph of f(x) = 5ª, write the equation of the graph that results when: (a) f(x) is…

A:

Q: Starting with the graph of f(x) = 9ª, write the equation of the graph that results from (a) shifting…

A:

Q: Starting with the graph of f(r) = 2", write the equation of the graph that results from a. shifting…

A:

Q: Starting with the graph of f(x) = 5ª, write the equation of the graph that results from a.…

A:

Q: Sketch the graph of the function: f(x,y)=10-4x-5y

A: Given:

Q: Starting with the graph of f(x) = 4", write the equation of the graph that results (a) f(æ) is…

A:

Q: y 8, f(x) -6-5-4-3-2–1 1 2 3 4 5 9 10 -2kb -3 Match the functions with its graph 1. a) y = - f(x-4)…

A: 1) a)  y= -f(x-4) y= f(x) ---&gt; y = -f(x) , the graph of y= f(x) will be reflected about x axis…

Q: (a) y = I+8

A: Solution is given below:

Q: Starting with the graph of f(x) = 9², write the equation of the graph that results when: (a) f(x) is…

A:

Q: Sketch the graph of f.

A: Given that

Q: Starting with the graph of f(x) = 9, write the equation of the graph that results from a. shifting…

A: The graph of y=f(x)-a shifts a units downward to  the graph of y=f(x). Where a&gt;0. The graph of…

Q: Starting with the graph of f(x) = 7*, write the equation of the graph that results from (a) shifting…

A: Given Data The equation is f(x) =7ˣ.   (a) The y-axis is located in an upward direction, so the…

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.