Chapter SH, Problem 3.10EP

To determine

To represent the $f(x)=x$stretched vertically by 4 and translate up 3 units.

Answer to Problem 3.10EP

Transformation of graph is $g(x)=4x+3$ .

Explanation of Solution

Given information:

  $f(x)=x$

  

Calculation:

Let $g(x)$be the indicated transformation of $f(x)$ .

In general, Vertical stretch of $f(x)$by factor a .

  $g(x)\to af(x)$

Then, the $f(x)=x$stretched vertically by 4 given below

  $g(x)=4x$

In general, translation of f(x) by up b units.

  $g(x)\to f(x)+b$

Then, translation of f(x) by up 3 units.

  $g(x)=4x+3$

Transformed graph, g(x) of f(x) is given below

  

Hence, the transformation is $g(x)=4x+3$ .