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Chapter 2: Q. 28 (page 125)

Is the graph shown the graph of a function?

Short Answer

Expert verified

The given graph is the graph of a function.

Step by step solution

01

Step 1. Concept Used 

The vertical line test states that a set of points in the plane is the graph of a function if and only if every vertical line intersects the graph in at most one point.

02

Step 2. Identify whether the graph is a function or not 

Draw a vertical line to the graph of the function.

It can be seen that each vertical line intersects the graph at atmost one point.

So the given graph is the graph of a function.

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Most popular questions from this chapter

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

True or False The domain of the function f(x)=x2-4xis{x|x≠±2}.

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

A rectangle is inscribed in a circle of radius of 2. See the figure. Let P=x,ybe the point in quadrant I that is a vertex of the rectangle and is on the circle.

Part (a): Express the area Aof the rectangle as a function of x.

Part (b): Express the perimeter pof the rectangle as a function of x.

Part (c): Graph A=Ax. For what value of xis Alargest?

Part (d): Graph p=px. For what value ofxis p largest?

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

hx=x+1
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