Question

The graph of f (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of h (in red).

The function f is defined by f(x)= sqrt x
Write down the expression for h(x)

Answer 1

\[y = f(x)+a\]is the graph of \[y = f(x)\]shifted vertically by \(a\) units
\[y = f(x-a)\] is the graph of \[y = f(x)\]shifted horizontally by \(a\) units

Answer 2

That's not right. It's -4 and it's in the square root,

Answer 3

ive been working on this since yesterday and it still isn't any clearer. ive also been reading other pieces of information on transformations.

Answer 4

can someone give me the solution and tell me why it works? I have like 12 more of these.

Answer 5

look at the graph,
for definiteness, pick one point : the thick solid point.

Answer 6

on blue graph, it is at (0, 0)
on red graph, it is at (4, 2)

right ?

Answer 7

that means

the point (0, 0) shifted to the point (4, 2) :

(0, 0) ---> (4, 2)

Answer 8

it seems,
x values are shifting "right" by 4 units,
and y values are shifting "up" by 2 units

Answer 9

would it be: \[f(x)=\sqrt{x-4}+2\] @ganeshie8

Answer 10

It would be. Just like I advised you initially:

\[f(x-4) + 2\]to shift horizontally by 4 and vertically by 2

Answer 11

what happens to the radical?

Answer 12

never mind I get it it goes under the radical. thank you..

Answer 13

The radical is still there. \[f(x) = \sqrt{x}\]\[f(x)+a = \sqrt{x}+a\]\[f(x-a) = \sqrt{x-a}\]

Answer 14

and \[f(x-a)+b = \sqrt{x-a}+b\]

Answer 15

think of \[f(x) = \sqrt{x}\]as a recipe. It means "whenever you see the expression \(f(expression)\), replace it with \(\sqrt{expression}\)"