Pre-Cal problem

Question

The shape of f(x)=|x|, but shifted 14 units up and then reflected in the x-axis

g(x)=

Answer 1

f(x) = | x |

f(x) = | x | + 14 shifted up 14 units

f(x) = -| x | + 14 reflected over x-axis

Answer 2

So, let's think about this. To get the function to teflect across the x-axis, we need to be the y-value, or g(x), to be the opposite of f(x), right? If f(6) = 2, then g(x) =-2, for example.

f(x) = |x|

First, we shift it up 14 units, so g(x) = |x| + 14

Then, we have to make the entire right side the opposite.

g(x) = -|x| - 14

Let's check.

f(4) = |4| = 4

g(4) = |4| + 14 = 4 + 14 = 18. We just shifted up 14.

g(4) = -|4| - 14 = -4 - 14 = -18. Hey, that's reflected across the x-axis.