Chapter 1.4, Problem 80E

(a)

To determine

To compare: The graph of $g(x)=a{x}^2$ with the graph of $f(x)=x^2$ .

Answer to Problem 80E

The graph of g(x) will expand at the interval of $0<a<1$

Explanation of Solution

Given data:

  $g(x)=a{x}^2$

  $f(x)=x^2$

Calculation:

When $0<a<1$

The graph of $g(x)=a{x}^2$ and graph of $f(x)=x^2$

  

Purple color is graph is of $f(x)=x^2$ and pink color is graph is of $g(x)=a{x}^2$

The graph of g(x) will expand at the interval of $0<a<1$

Conclusion:

The graph of g(x) will expand at the interval of $0<a<1$

(b)

To determine

To compare: The graph of $g(x)=a{x}^2$ with the graph of $f(x)=x^2$ .

Answer to Problem 80E

The graph of $g(x)=a{x}^2$ will start contracting when $a>1$ .

Explanation of Solution

Given data:

  $g(x)=a{x}^2$

  $f(x)=x^2$

Calculation:

When $a>1$

The graph of $g(x)=a{x}^2$ and graph of $f(x)=x^2$

  

Purple color is graph is of $f(x)=x^2$ and pink color is graph is of $g(x)=a{x}^2$

The graph of $g(x)=a{x}^2$ will start contracting when $a>1$ .

Conclusion:

The graph of $g(x)=a{x}^2$ will start contracting when $a>1$ .