(a) Consider the graphs of y1 = f(x) and y2 = f(2x + 7). Make a prediction about how these graphs are related. In particular what does the graph of y2 = f(2x + 7) look like in comparison to y1 = f(x)? (b) Suppose that, in addition, we know that f(x) = x2. Graph y1 = f(x) and y2 = f(2x + 7). Make sure you measure the horizontal distance between the vertices of the two graphs. How do your findings fit with your expectations from part a)

Q: Use the graph of f(x) = √x to obtain the graph of g(x) = √(x - 4)

A: We first graph the parent function  f(x) = √x

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A:

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A:

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Q: Sketch

A:

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A:

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Q: How are the graphs of f(x) = x and g(x) = -f(x) – 1 related?

A:

Q: What is the effect on the graph of f(x)= x when g(x)= + 4?

A: when you add +4 in function  e.g f(x)=x g(x)=f(x+4)=x+4

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.