A researcher models the depth of a sediment layer, $D (p)$ , in millimetres as a function of the pressure $p$ in kilopascals using the modulus function:

\quad p \ge 0

where $c$ is a positive constant representing the compression coefficient.

The graph of $y = D (p)$ has a minimum point $M$ and intersects the $y$ -axis at the point $S$ .

(i) Find the $y$ -coordinate of $S$ . (ii) Find, in terms of $c$ , the $p$ -coordinate of $M$ .

Find, in terms of $c$ , the set of values of $p$ for which the sediment depth is negative.

A second model suggests the depth follows the linear relationship $y = 18 - 4 p$ . Given that this linear model intersects the modulus model $y = D (p)$ at two distinct points,

find the range of possible values for $c$ .

A researcher models the depth of a sediment layer, $D (p)$ , in millimetres as a function of the pressure $p$ in kilopascals using the modulus function:

\quad p \ge 0

where $c$ is a positive constant representing the compression coefficient.

The graph of $y = D (p)$ has a minimum point $M$ and intersects the $y$ -axis at the point $S$ .

(i) Find the $y$ -coordinate of $S$ . (ii) Find, in terms of $c$ , the $p$ -coordinate of $M$ .

Find, in terms of $c$ , the set of values of $p$ for which the sediment depth is negative.

A second model suggests the depth follows the linear relationship $y = 18 - 4 p$ . Given that this linear model intersects the modulus model $y = D (p)$ at two distinct points,

find the range of possible values for $c$ .

Functions and Graphs

Question 23

Markscheme

Functions and Graphs

Question 23

Markscheme

Functions and Graphs

Question 23

Functions and Graphs Questions

Functions and Graphs

Question 23

Functions and Graphs Questions