Chapter 2.5, Problem 34AYU

In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of $y\text{ = }\sqrt{x}$ in the order stated.

If $\left(4,\text{ 2}\right)$ is a point on the graph of $y\text{ = }f\left(x\right)$, which of the following points must be on the graph of $y\text{ = 2}f\left(x\right)$?

a. $\left(4,\text{ 1}\right)$     b. $\left(8,\text{ 2}\right)$

c. $\left(2,\text{ 2}\right)$     d. $\left(4,\text{ 4}\right)$

To determine

To find: The points on the graph of $y=f\left(2x\right)$ if $\left(4,2\right)$ is a point on the graph of $f(x)$.

Answer to Problem 34AYU

The point is $\left(2,2\right)$.

Explanation of Solution

Given:

$y=f\left(x\right)$; and the point is $\left(4,2\right)$

$y=f\left(2x\right)$ means horizontally shifted by a factor 2

Multiply by $\frac{1}{2}$ on the each $x\text{-coordinate}$ of the graph of $y=f\left(x\right)$.

Hence the point is $\left(2,2\right)$.