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Chapter 1: 1.1-8E (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 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

Biologists have noticed that the chirping rate of crickets of a certain species is related to temperature, and the relationship appears to be very nearly linear. A cricket produces 113 chirps per minute at\({\bf{7}}{{\bf{0}}^{\bf{o}}}{\bf{F}}\)and 173 chirps per minute at\({\bf{8}}{{\bf{0}}^{\bf{o}}}{\bf{F}}\).

(a) Find a linear equation that models the temperature T as a function of the number of chirps per minute N.

(b) What is the slope of the graph? What does it represent?

(c) If the crickets are chirping at 150 chirps per minute, estimate the temperature

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

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

Express the function in the form \({\bf{f}} \circ {\bf{g}}\)

\({\bf{F}}\left( {\bf{x}} \right){\bf{ = }}{\left( {{\bf{2x + }}{{\bf{x}}^{\bf{2}}}} \right)^{\bf{4}}}\)

A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.
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