need help with compressions and expansions. will fan and medal

Question

owlstudies · Answer

$$f(x)=\sqrt[3]{2x+6}-7$$

owlstudies · Answer

for example, what would be the translation and compression or expansion in the problem above^^

unklerhaukus · Answer

can you recognise the parent function?

owlstudies · Answer

cube root of x?

unklerhaukus · Answer

yeah

owlstudies · Answer

so would it be down seven, left six? I understand that but i don't understand what to do with the 2x part of it

unklerhaukus · Answer

down by seven is right

unklerhaukus · Answer

but the argument of the function is   2x+6,   i.e.  2(x+3)

unklerhaukus · Answer

so what is the horizontal translation ?

owlstudies · Answer

left 3

unklerhaukus · Answer

yes!

unklerhaukus · Answer

The 2 makes all the x values half as big, for the same y values
in other words there is a horizontal compression

owlstudies · Answer

why does it make all the values half as big?

unklerhaukus · Answer

For the left hand side to remain the same,  the argument of the function must be the same, so f(2x) must move through the value twice as fast as f(x)

owlstudies · Answer

okay that makes sense thnank you