In this question you will be assessed on using good English, organising information clearly and using specialist terms where appropriate. The information in the box is about the properties of solids and gases.

Solids:
• have a fixed shape
• are difficult to compress (to squash).
Gases:
• will spread and fill the entire container
• are easy to compress (to squash).
Use your knowledge of kinetic theory to explain the information given in the box.
You should consider:
• the spacing between the particles
• the movement of individual particles
• the forces between the particles.

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.