Functions and Graphs

A specialized hydraulic piston's displacement $D$ (in mm) relative to a benchmark is modeled by the equation:

\frac{2}{5}|5t + 8| - 6, \quad t \in \mathbb{R}

where $t\,$ is the time in seconds.

a.

State the coordinates of the vertex, $V$ , of the graph of $y = D (t)$ .

[2]

b.

Using algebra, determine the set of values of $t\,$ for which

\frac{1}{5}t

[4]

c.

Sketch the graph with equation $y = ∣ D (t) ∣$ , stating the coordinates of the local maximum point and each local minimum point.

[4]

A specialized hydraulic piston's displacement $D$ (in mm) relative to a benchmark is modeled by the equation:

\frac{2}{5}|5t + 8| - 6, \quad t \in \mathbb{R}

where $t\,$ is the time in seconds.

a.

State the coordinates of the vertex, $V$ , of the graph of $y = D (t)$ .

[2]

b.

Using algebra, determine the set of values of $t\,$ for which

\frac{1}{5}t

[4]

c.

Sketch the graph with equation $y = ∣ D (t) ∣$ , stating the coordinates of the local maximum point and each local minimum point.

[4]

Functions and Graphs Questions