The diagram show the graph of the function y = f(x) where S(x) =(x+1)° – 3 for the domain -4sxs2 The function has a minimum value at B. (i) Find the coordinates of A, B and C. ii) State the range of f (x) iii) Explain why f(x) is a many-to-one function.

Q: Use the graph of y = f(x) to graph y = f(x - 2) - 1.

A: The objective is to plot the graph of y=fx-2-1 by using the graph y=fx. From the given graph, by…

Q: 3. Let f(x) = 3x² + 1 and g(x) = x + 4. Find (f+g)(x) and (f- g)(x) and state the domain of each.

A: Given,

Q: If  f(a)=b,  then which point is on the graph of   f(x)? 1. (f(a),f(b)) 2. (a, b)(a,b) 3.…

A: Given : f(a) = b

Q: For the graph above, find f(-2) f(-2) =

A: Here Y = f(X) is representing the equation of the graph shown above.   We can clearly observe that…

Q: Sketch the graph of the function. f(x, v) = y? + 7

A:

Q: 6. f (x) 7. f-1 (x) y y 1 1 -1 -1 -2

A:

Q: Estimate f(g(2)): First graph y=f(x) Second graph y=g(x)

A:

Q: 3. Let f(x) = 3x² + 1 and g(x) = x + 4. Find (f+g) (x) and (f- g)(x) and state the domain of each.

A:

Q: Graph the function F(x)=1/2x-4. Use a line to draw the line x=4 and then use a dot to graph the…

A:

Q: 5- Draw the graph of y=f(x) and Y=1/f(x)on the same axes. State the domain, a range of reciprocal…

A: For a function y=f(x), the set of real values of x for which f(x) is defined is called the domain of…

Q: Find the domain and range of y=f(x)

A: To find the domain and range of y=fx

Q: 2. (a) On graph paper, using the same axes, draw and label the graphs of the following equations.…

A: We take x-axis as horizontal line and y-axis as vertical line in order to draw and label the given…

Q: 4. (a) {(x, y)|y = (x – 1)² + 2} (b) {(x. y) | x = (y – 2) + 1} (c) {(x, y) | y = (r + 2)' - 1} (d)…

A: (a) Given that x,y:y=x-12+2 The function f(x)=(x-1)2+2. The domain for the function is (-∞,∞). (b)…

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.