Question

Write an equation for the following transformation of y=x: a vertical stretch by a factor of 4.

Answer 1

y=4x

Explanation:

We are given a equation of line, y=x

We need to find the equation of new line whose vertical stretch by a factor of 4.

`y=f(x)`

For vertical stretch or compress

`y=a\cdot f(x)`

If a>1 then vertical stretch

If 0<a<1 then vertical compress

Here vertical stretch by factor of 4

`y=4f(x)`

`y=4x`

New equation becomes y=4x

Hence, The equation of transform line is y=4x

Answer 2

Vertical stretch by a factor of 4 means we have to transform the function by a unit of 4.

Given function is F(x)=x

Transformed function is ,y=4x

y=x , implies that the line is passing through origin having slope of 45°

y=4x, means the function has stretched by four units having slope 4 units or
`\tan^(-1)4`.