By analyzing the shown graph, we conclude that it is a absolute value function:
f(x) = -|x + 1| + 1
What is the equation that matches the graph?
In the graph, we can see an absolute value function that opens downwards, has a slope of 1 unit, and has a vertex on the point (-1, 1).
Then, because of the vertex, we know that we have something like:
f(x) = a*|x + 1| + 1
Because the slope is 1, and the function opens down, we know that "a" must have a module of 1 and a negative sign, then:
a = -1
Then the equation for the shown graph is:
f(x) = -|x + 1| + 1
If you want to learn more about absolute value functions, you can read:
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