Use the given graph of f to find a number δ such that if 0 < |x − 3| < δ then |f(x) − 2| < 0.5

Question

Use the given graph of f to find a number δ such that if 0 < |x − 3| < δ then |f(x) − 2| < 0.5

δ = _______

Answer 1

For f(x), the y-value, to be less than 0.5 from 2,

(that is between the two horizontal red lines)

the x-value must be between 2.6 and 3.8

(that is between the two vertical red lines)

2.6 < δ < 3.8

Answer 2

If 0 < |x − 3| < δ then 3 - δ < x < 3 + δ, so 3 - δ = 2.6, δ = 0.4; so 0 < δ ≤ 0.4