Question

Write an algebraic equation to match each graph. (These graphs are not drawn to scale!) please help! i will make brainliest answer if correct!

Answer 1

Answer:

the expression of this function is:

$f(x)=|x-1|-1$

Step-by-step explanation:

This graph corresponds to an absolute value function, which as you can see has the minimum (vertex) at the point (1, -1) on the plane, and also that goes through the origin of coordinates (0, 0)

therefore, notice that from the point (0, 0) to (1, -1) there is a slope of "-1" which is going to characterize the steepness of the x- variable that resides inside the absolute value function. since the vertex has also moved from the characteristic (0, 0) in the function:

$f(x)=|x|$

then we have to include a horizontal shift to the right in one unit (by subtracting 1 units from x), and a vertical shift  downwards one unit (by subtracting 1 from the full absolute value expression) in order to shift the vertex to the position (1, -1):

$f(x)=|x-1|-1$