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Chapter 1: Q5E (page 8)

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.

Short Answer

Expert verified

The curve is not a graph of the function.

Step by step solution

01

Vertical line test

A graph is said to be the graph of a function of x if and only if no vertical line intersects the curve more than once.

02

Determine whether the curve is the graph of a function of x

Draw a vertical line as follows.

From the given graph, it can be clearly seen that if a vertical line is drawn on the curve, then the line will intersect the graph more than once.

Therefore, the curve is not a graph of the function.

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Most popular questions from this chapter

The graph shown gives the weight of a certain person as a function of age. Describe in words how this person’s weight varies over time. What do you think happened when this person was 30 years old?

Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.

An airplane takes off from an airport and lands an hour later at another airport, 400 miles away. If trepresents the time in minutes since the plane has left the terminal, let \(x\left( t \right)\)be the horizontal distance traveled and \(y\left( t \right)\) be the altitude of the plane.

(a) Sketch a possible graph of\(x\left( t \right)\).

(b) Sketch a possible graph of\(y\left( t \right)\).

(c) Sketch a possible graph of the ground speed.

(d) Sketch a possible graph of the vertical velocity.

Find\(fogoh\)

\(f\left( x \right) = \sqrt {x - 3} \), \(g\left( x \right) = {x^2}\), \(h\left( x \right) = {x^3} + 2\)

Prove the statement using the \(\varepsilon ,\)\(\delta \)definition of a limit and illustrate with a diagram like a Figure 15.

\(\mathop {\lim }\limits_{x \to 3} \left( {1 + \frac{1}{3}x} \right) = 2\)
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