Question

need help with compressions and expansions. will fan and medal

Answer 1

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

Answer 2

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

Answer 3

can you recognise the parent function?

Answer 4

cube root of x?

Answer 5

yeah

Answer 6

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

Answer 7

down by seven is right

Answer 8

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

Answer 9

so what is the horizontal translation ?

Answer 10

left 3

Answer 11

yes!

Answer 12

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

Answer 13

why does it make all the values half as big?

Answer 14

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)

Answer 15

okay that makes sense thnank you