Question

Write an equation to match the graph:

Answer 1

Answer:

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

Step-by-step explanation:

This is an absolute value equation, because it's that v-shape that let's us know it will be one. The standard form is

f(x)= a|x - h| + k, where h is the horizontal shift, k is the vertical shift, and a is the dilation factor.

We know that the graph is moved up one, because its vertex is at y = 1. So k = 1.

f(x)= a|x - h| + 1

We also know that it must be negative, because it's upside-down, so put the negative outside the absolute value, not inside.

f(x)= -|x - h| + 1

Lastly, the horizontal shift is left one, so we know that h = -1.

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

x minus a negative one equals x plus one, so

f(x)= -|x + 1| + 1 is our final answer.