Question

What function g describes the graph of f after the given transformations? f(x)=|x| +8; reflected across the x-axis and translated 10 units up

Answer 1

the function g that describes the graph of f after the given transformations is: g(x) = -|x| + 2

To reflect the graph of f(x) = |x| + 8 across the x-axis, we need to negate the function, which gives us:

-g(x) = -(|x| + 8) = -|x| - 8

To translate this function 10 units up, we need to add 10 to the function, which gives us:

g(x) = -|x| - 8 + 10 = -|x| + 2

Therefore, the function g that describes the graph of f after the given transformations is: g(x) = -|x| + 2