Question

Help please? Compared to the graph of the function `f(x) = sqrtx`, how is the graph of `g(x)= sqrt(x+8)-4` translated?

Answer 1

C

Explanation:

It has been shifted down `4` units and to the left `8` units

`f(x)=sqrt(x+-a) rarr` If the number that is altering the function is inside the square root, then the function is being shifted right (if something is being subtracted) or shifted left (if something is being added)

Here, the function is being horizontally shifted 8 units left

`f(x)=sqrtx+-b rarr` If the number that is altering the function is outside the square root, then the function is being shifted up (if something is being added) or shifted down (if something is being subtracted)

Here, the function is being vertically shifted 4 units down

Answer 2

`\sqrt{x+8}-4` is `\sqrt{x}` shifted `8` to the left, `4` down, choice C.

Explanation:

It's confusing, but I just think of `y=x^2` for these shifting in `x` and `y`. `y=(x+8)^2` has a its vertex at `x=-8,` so adding to `x` shifts to the left, more negative `x`.

`y=x^2 -4`, where we're shifting the `y` value, has a minimum at `y=-4` instead of `y=0`, so by subtracting four we've translated `4` down.

`\sqrt{x+8}-4` is `\sqrt{x}` shifted `8` to the left, `4` down, choice C.

Let's just pop this into Socratic's grapher and make sure.

graph{sqrt(x+8) -4 [-8.71, 11.29, -5.12, 4.88]}