Chapter 1.2, Problem 4GP

Solution

To compare: The graph of the function $y=\frac{1}{6500}{(x-1400)}^2+27$ with the graph of the function $y=\frac{1}{7000}{(x-1400)}^2+27$ given in the example.

The graph of the function $y=\frac{1}{7000}{(x-1400)}^2+27$ is compressed in x-direction to give the graph of the function $y=\frac{1}{6500}{(x-1400)}^2+27$ .

Given information:

The function $y=\frac{1}{6500}{(x-1400)}^2+27$ and the graph of the function $y=\frac{1}{7000}{(x-1400)}^2+27$ .

Concept used:

For a function of the type $y=\text{C}\cdot f\left(x\right)$ , if $\text{C}>1$ , it compresses the function in the x-direction and if $0<\text{C}<1$ , it stretches the function in x-direction.

Calculation:

Use graphing calculator to graph the functions follows:

  

Observe that the graph of the function $y=\frac{1}{7000}{(x-1400)}^2+27$ is compressed in x-direction to give the graph of the function $y=\frac{1}{6500}{(x-1400)}^2+27$ .

Conclusion:

The graph of the function $y=\frac{1}{7000}{(x-1400)}^2+27$ is compressed in x-direction to give the graph of the function $y=\frac{1}{6500}{(x-1400)}^2+27$ .