Question

Describe the transformations of f(x) when compared to the parent function. f(x)=(x+7) a) horizontal shift left 7 units b) horizontal shift right 7 units c) vertical shift up 7 units d) vertical shift down 7 units

Answer 1

We have the function:

$f(x)=x+7$

The parent function is the linear parent function p(x)=x.

We can see that f(x) is 7 units above p(x) for any value of p(x), so we can transform p(x) to f(x) by a translation of 7 units in the y-axis.

We can see this in the graph:

Then, the transformation is a vertical shift up 7 units.