Functions and Graphs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88

Question 45

The temperature $T$ (in $∘C^{\circ}\text{C}$ ) of a chemical reaction at time $t\,$ minutes is modeled by a continuous piecewise linear function $T = f (t)$ . The graph of $T = f (t)$ is described as follows:

For $\le -2$ , the temperature is constant at $T = - 3$ .
For $\le t \le 4$ , the temperature increases linearly from $(- 2, - 3)$ through $(0, 1)$ to $(4, 9)$ .
For $\ge 4$ , the temperature remains constant at $T = 9$ .

a.

Sketch the graph of $y = f (- t)$ .

[2]

b.

Sketch the graph of $y = 2 f (t) - 5$ .

[2]

c.

Sketch the graph of the derivative $y = f^{'} (t)$ .

[2]

Functions and Graphs

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88

Question 45

The temperature $T$ (in $∘C^{\circ}\text{C}$ ) of a chemical reaction at time $t\,$ minutes is modeled by a continuous piecewise linear function $T = f (t)$ . The graph of $T = f (t)$ is described as follows:

For $\le -2$ , the temperature is constant at $T = - 3$ .
For $\le t \le 4$ , the temperature increases linearly from $(- 2, - 3)$ through $(0, 1)$ to $(4, 9)$ .
For $\ge 4$ , the temperature remains constant at $T = 9$ .

a.

Sketch the graph of $y = f (- t)$ .

[2]

b.

Sketch the graph of $y = 2 f (t) - 5$ .

[2]

c.

Sketch the graph of the derivative $y = f^{'} (t)$ .

[2]

Functions and Graphs

Question 45

Functions and Graphs Questions

Functions and Graphs

Question 45

Functions and Graphs Questions