Question

Give me the points of f(x)=-0.5|x+1|+2. Determine whether the function has its minimum or maximum values so you can place your first point there

Give two points

Answer 1

1. To find the minimum or maximum value of the function f(x) = -0.5|x+1| + 2, we need to analyze the absolute value term. The absolute value function |x+1| will be at its minimum value when x+1 = 0, i.e., when x = -1. Therefore, the function f(x) will have its maximum or minimum value at x = -1.

2. To find the value of f(x) at x = -1:
f(-1) = -0.5|-1 + 1| + 2
f(-1) = -0.5|0| + 2
f(-1) = 2

Therefore, the point (-1, 2) is where the function f(x) = -0.5|x+1| + 2 has either its minimum or maximum value.

3. To find another point, we can choose another x-value and calculate the corresponding y-value. Let's choose x = 0:
f(0) = -0.5|0 + 1| + 2
f(0) = -0.5|1| + 2
f(0) = -0.5 + 2
f(0) = 1.5

The point (0, 1.5) is another point of the function f(x) = -0.5|x+1| + 2.