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Chapter 1: Q9E (page 7)

Make a rough sketch by hand of the graph of the function. Use the graphs given in Figures 3 and 15 and, if necessary, the transformations of Section 1.3.

9. \(g\left( x \right) = {{\bf{3}}^x} + {\bf{1}}\)

Short Answer

Expert verified

The graph of the function \(g\left( x \right) = {3^x} + 1\) is obtained from the graph of \(g\left( x \right) = {3^x}\) after the following transformation:

  • Shift the graph 1 unit upward.

Step by step solution

01

Write the transformation to find the graph of \(g\left( x \right) = {{\bf{3}}^x} + {\bf{1}}\)

The graph of the function \(g\left( x \right) = {3^x} + 1\) is obtained from the graph of \(g\left( x \right) = {3^x}\) after the following transformation:

  • Shift the graph 1 unit upward.
02

Sketch the graph of transformation from \(g\left( x \right) = {{\bf{3}}^x}\) and \(g\left( x \right) = {{\bf{3}}^x} + {\bf{1}}\)

The figure below represents the graph of \(g\left( x \right) = {3^x}\):

The figure below represents the graph of \(g\left( x \right) = {3^x} + 1\):

Thus, the graph of the function is obtained.

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Most popular questions from this chapter

The point \(P\left( {{\bf{2}}, - {\bf{1}}} \right)\) lies on the curve \(y = \frac{{\bf{1}}}{{{\bf{1}} - x}}\).

(a) If Q is the point \(\left( {x,\frac{{\bf{1}}}{{{\bf{1}} - x}}} \right)\), find the slope of the secant line PQ (correct to six decimal places) for the following values of x:

(i) 1.5 (ii) 1.9 (iii) 1.99 (iv) 1.999 (v) 2.5 (vi) 2.1(vii) 2.01 (viii) 2.001

(b) Using the results of part (a), guess the value of the slope of tangent line to the curve at \(P\left( {{\bf{2}}, - {\bf{1}}} \right)\).

(c) Using the slope from part (b), find an equation of the tangent line to the curve at \(P\left( {{\bf{2}}, - {\bf{1}}} \right)\).

The graph of a function \(g\) is given.

(a) State the values of \(g\left( { - {\bf{2}}} \right)\), \(g\left( {\bf{0}} \right)\), \(g\left( {\bf{2}} \right)\), and \(g\left( {\bf{3}} \right)\).

(b) For what value(s) of x is \(g\left( x \right) = {\bf{3}}\)?

(c) For what value(s) of x is \(g\left( x \right) \le {\bf{3}}\)?

(d) State the domain and range of g.

(e) On what interval(s) is g increasing?

Determine whether f is even, odd, or neither. You may wish to use a graphing calculator or computer to check your answer visually.

86. \(f\left( x \right) = {\bf{1}} + {\bf{3}}{x^{\bf{3}}} - {x^{\bf{5}}}\)

Figure 1 was recorded by an instrument operated by the California Department of Mines and Geology at the University Hospital of the University of Southern California in Los Angeles. Use it to estimate the range of the vertical ground acceleration function at USC during the Northridge earthquake.

15-18 determine whether the curve is the graph of a function of \(x\). If it is, state the domain and range of the function.

16.
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