How do you know scientifically that fat and soap are different substances?

Soap is soluble in water, but fat is not. Fat has a melting point above 47C and soap has a melting point above 100C. Fat has a density of 0.92 g/cm3 and soap has a density of 0.84 g/cm3. These are all properties that make fat and soap different substances.

Explanation:

answer-

the statement that f(x) = |x+a| + b has exactly one x-intercept is sometimes correct.

solution-

it solely depends on b, whether the function will have one or two or zero x intercept.

this plot of the given function, f(x) = |x+a| + b will be the basic absolute value graph i.e v shape, with vertex translated to (-a, b), instead of origin.

1-   if b is zero, the graph will have exactly one x-intercept, at x= -a

2- if b is positive, the whole graph will be above the x-axis, hence it will have no x-intercepts.

3- if b is negative, the graph will be below the x-axis, hence it will have two x-intercepts.

∴ the statement is sometimes true.