Use transformations of f(x) =x2 to graph the follow h(x) = (x - 6)2 + 3 %3D Stretch the graph vertically by a factor of 6. Shift the graph 3 units up. Shift the graph 6 units to the right. Reflect the graph about the y-axis. Reflect the graph about the x-axis. Shrink the graph horizontally by a factor of 3. Use the graphing tool to graph the functron.

Q: The graph of y= f (-x)-2 is the graph of y= f(x) 1. A. reflected over the x-axis and shifted down 2…

A: Explained below

Q: Q3/ Sketch the graph of f(x) = x+1

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Q: 10. Graph the step function: f(x)=[x]+[x]. (Hint: Use an xy-table of values.)

A: Given : f(x) = x + x.   To graph the step function f(x) = x + x.

Q: The graph of f(x) = x² is shifted 3 units to the left. This graph is then vertically shrunk by a…

A: Given: f(x)=x2 shifted 3 units left vertically shrunk=15along x-axis shifted downwards by7 units

Q: Look at the graph of: ` y = Vx – 1+ 3 %3D What is the starting point of the graph? What is the…

A:

Q: Use your calculator to graph the function f (x) = x – 2x² - 8 using a window of xmin = -8, xmax = 8,…

A:

Q: Consider the following. x2 + y2 = 4 (a) Find two explicit functions by solving the equation for y in…

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Q: Graph t(x) = (x – 2)³ + 1 by starting with the graph of y = x³ and using transformations.

A: We know that the graph of y=x3 can be plotted on co-ordinate axis as

Q: 16. Graph the function f(x) = -3x + 7.

A: The given function is: fx=-3x+7 This is a linear function, which represents the line. To graph, this…

Q: Sketch the graph of glx) = 2?J x + . Support the graph by a table

A:

Q: Identify the vertex of the following.f(x) = x2 − 4Use a graphing utility to verify your results.(x,…

A: Important points: 1. To find the vertex, first we will write the given equation in a parabola…

Q: 10. Graph the function. f(x) = -2(x- 4)(x + 2) %3D

A: Topic = Parabola

Q: 3. If g(x) = log, (3x+ 4) a) Graph g(x) b) Identify the vertical asymptote of g(x) c) What is the…

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Q: What is the function of the graph? Select the correct answer. Oy-x? - 82? + 5x Oy-6x-8x3 + 5x y-x° -…

A: Facts : 1. Complex roots always occur in conjugate pair. 2. If the polynomial has degree 'n' : A. n…

Q: skecth the graph a) f(x)=(x-2)2(x+3)   b)f(x) = x2-1/x   c)f(x) = 2x/x2-1    d)f(x) = -23 + 7x2 - 2x…

A: To sketch the graph of given function :

Q: The point (214) is on the Graph of y =f() The point on the graph of y-gl), where glx) = f(xt 7) IS?…

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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: The graph of f(x) = x2 – 7 is horizontally stretched by a factor of 4.5. Write the equation…

A: Here the graph of f(x)=x²-7 is horizontally stretched by a factor of 4.5.  We want to write the…

Q: The table to the right shows the electricity rates charged by Better Than Lightning Utilities in the…

A: For x>500 ,  w(x) = Base price + 500*(Price below 500 kwh) + (x-500) * (price above 500 kwh)

Q: Determine whether the graphs of the following equations and functions are symmetric about the…

A: We have to determine whether the graphs of the following equations and functions are symmetric about…

Q: y=(2)+2 • Use tvanstormation to describe how the gvaph is related to an exponential fenetion •Sketch…

A: Consider and exponential function;  y=12x Now draw the graph of y=12x at points given in the table;…

Q: Starting with the graph of f(x) = 5°, write the equation of the graph that results when: %3D (a)…

A: f(x) = 5x

Q: Compared with the graph of f(x) the graph of x' 1 g(x) : 1 is shifted 2 units , and x + 2 1 unit

A: Given : Compared with the graph of f(x) = 1x , the graph of g( x) =1x + 2 - 1 is shifted 2 units…

Q: Draw the graph of g(x) = f(x + 3) below. The graph of y = f(x) is shown below. After finishing the…

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Q: Find the inverse of ƒ(x) = x + b (b constant). How is the graph of ƒ -1 related to the graph of ƒ?

A: To find the inverse we plug f(x)=y Then switch x and y and solve for y

Q: Look at the graph of: y = Vx - 3 %3D What is the starting point of the graph? What is the domain?…

A: Given graph Y = √(X-3)

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

A: f(x) = 9x a) f(x) is shifted 7 units downward, y = (9x - 7)

Q: y=1/2cot3x graph trig function

A:

Q: Your friend attempted to graph the equation f(x)=-2cos(1/3(x-60))+3. Based on their graph of the…

A: The base function is  where x is in degrees Now we have the transformation So, the amplitude of the…

Q: The table to the right shows the electricity rates charged by Better Than Lightning Utilities in the…

A: NOTE: Refresh your page if you can't see any equations. . the base charge is $6.5 and for the first…

Q: c. If A(x) = x² In(f(x)), what is the value of A'(2)? What does this result say about the behavior…

A:

Q: The graph of f (x) = x² was transformed to create the graph of g(x) = – (6x)² . Which of these…

A: f(x) = x2g(x) = -(6x)2

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

A:

Q: Let k eR and f(x, y) = x² + y² + kxy. If you imagine the graph changing as k increases, at what…

A: We have to find k such that the graph changing as ke increases, at what values of k does the shape…

Q: Approximate the value of g"(0.5). Giving a reason for your answer, what does this value say about…

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Q: Identify the vertex of the following.  f(x) = −x2 − 4x + 2Use a graphing utility to verify your…

A: Compare the given function with y=ax2+bx+c a=-1, b=-4, c=2 For vertex:

Q: Begin by graphing the square root function, f(x) = /x. Then, use transformations of this graph to…

A: To transform any function to any other desired function, we can use a combination of reflection,…

Q: The cube root parent function y = Va has been transformed. What is the equation of the new image? -5…

A:

Q: Identify the vertex of the following.f(x) = (x − 6)2 + 3Use a graphing utility to verify your…

A: f(x) = (x − 6)2 + 3 is in vertex form  We compare it with  f(x)=a(x-h)2+k  So, h=6 and k=3    So,…

Q: V3 1, a -1

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Q: 28. Use the graph below to determine the equation of h(x).

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Q: The graph of y= f(x-3) is the graph of y= f(x) 4 A. vertically compressed by a factor of 4 and…

A: Given function y=14f(x-3) with parent function y=f(x).

Q: (b) vertically stretching the graph by a factor of 4 of f(x) = Vĩ and then vertically shifting the…

A: we have to write an equation that represents the transformation formed by the following items B)…

Q: x < 0 6. Sketch the graph of f(x) = x2, x 20

A: Solution: The objective is to graph the given function

Q: Draw the graph of g(x) = f(x + 2) below. After finishing the graph, click outside the grid to stop…

A: Known fact: The graph of y=fx+a, a&gt;0 can be obtained by shifting the graph y=fx, a units left…

Q: Find the vertical asymptote (if any) of the graph of the function 2р + 3 (a) h(p) = р? — 49 7x (b)…

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Q: Begin by graphing the square root function, f(x) = /x. Then, use transformations of this graph to…

A: We have the square root function: f(x) = √x We need to transform this function to the new function:…

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

A:

Q: The table to the right shows the electricity rates charged by Better Than Lightning Utilities in the…

A:

Q: 16. Graph the function f(x)=- (2)*– 3

A: The given function is , fx=142x-3

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.