Chapter 9.2, Problem 31PPS

a.

To determine

To Analyze Graphical: graph of f (bx) for b =-3,-1, 0.25, 0.5,1,2, and 3.

Answer to Problem 31PPS

Explanation of Solution

Given information: Given $f(x)=x^2$ .

Calculation:

Graph of $f(bx)={(bx)}^2$for b =-3,-1, 0.25, 0.5,1,2, and 3 using a graphing calculator is shown below.

  

b.

To determine

To Analytical: describe the transformation from f(x) to f (bx) when b >1.

Answer to Problem 31PPS

Horizontally compressed.

Explanation of Solution

Given information: Given $f(x)=x^2$ .

Calculation:

From the graph, shown again below, when b > 1 (black and red), the graphs are narrower than $f(x)=x^2$ (blue in the right graph) so they are f(x) horizontally compressed.

Graph of $f(bx)={(bx)}^2$for b =-3,-1, 0.25, 0.5,1,2, and 3 using a graphing calculator is shown below

  

c.

To determine

To Analytical: describe the transformation from f(x) to f(bx) when 0< b<1.

Answer to Problem 31PPS

Horizontally stretched.

Explanation of Solution

Given information: Given $f(x)=x^2$ .

Calculation:

From the graph, shown again below, when 0 < b < 1 (green and orange), the graph is less narrow than $f(x)=x^2$ (blue in the right graph) so they are f(x) horizontally stretched.

Graph of $f(bx)={(bx)}^2$for b =-3,-1, 0.25, 0.5,1,2, and 3 using a graphing calculator is shown below.

  

d.

To determine

To Analytical: describe the transformation from f(x) to f (bx) when b <0.

Answer to Problem 31PPS

Sign of b has no affect.

Explanation of Solution

Given information: Given $f(x)=x^2$ .

Calculation:

From the graph, shown again below, when b < 0 , the graphs are the same as the corresponding positive values of b, that is $f(-x)={(-x)}^2=x^2=f(x)$ (blue in the both graphs) and $f(-3x)=f(3x)$ (red in both graphs). The sign of b then does not affect the graph, only the value of $\left|b\right|$ affects it.

Graph of $f(bx)={(bx)}^2$for b =-3,-1, 0.25, 0.5,1,2, and 3 using a graphing calculator is shown below.

  

e.

To determine

To Analyze Graphical: graph of af(x) for a =-2,-0.5, 0.5, and 3

Answer to Problem 31PPS

Explanation of Solution

Given information: Given $f(x)=x^2$ .

Calculation:

Using a graphing calculator, graph $y=af(x)=a{x}^2$ for a = -2(red), a = -0.5(blue),

a = 0.5(green), a = 3(orange),