To determine The graph, domain, range and equation of the asymptote for the function f ( x ) = − 1.5 x and state whether the function is increasing or decreasing on its domain. Explanation Given: The function is f ( x ) = − 1.5 x . Calculation: The function is given as follows: f ( x ) = − 1.5 x The above function is an exponential function of the form f ( x ) = a x , where a = − 1.5 . Since, the value of a is less than 1 so the curve of the given function is continuously decreasing. Draw the graph of the function f ( x ) = − 1.5 x . Figure 1 represents the graph of the function f ( x ) = − 1.5 x with y intercept as − 1 and no x intercept. The function f ( x ) = − 1.5 x is defined for all values of x and from the figure 1 it is observed that the value of the given function continuously decreases as the value of x is increased. So, the domain of the function f ( x ) = − 1.5 x is ( − ∞ , ∞ ) . From figure 1 it is observed that the curve of the function f ( x ) = − 1.5 x always lies below the x − axis or it can be said that the value of the given function is always negative for any defined value of x . So the range of the function f ( x ) = − 1.5 x is ( − ∞ , 0 ) . The curve of the function f ( x ) = − 1.5 x does not intersect the x − axis but as x → − ∞ then y → 0

7th Edition

ISBN: 9780134696522

Author: HORNSBY, John, Lial, Margaret L., Rockswold, Gary K.

Publisher: Pearson Education, Inc.,

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Chapter 6.2, Problem 21E

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The graph, domain, range and equation of the asymptote for the function f(x)=−1.5x and state whether the function is increasing or decreasing on its domain.

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Chapter 6.2, Problem 20E

Chapter 6.2, Problem 22E

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