Graphing functions

High School Math 1 · Unit 11 · function-features

function-features

Name ______________________________Date ______________

1.
A piecewise function is defined by

$f(x) = \begin{cases} x + 3 & \text{if } x < 0 \\ 2x & \text{if } x \ge 0 \end{cases}$

Find $f(-2)$ .
Answer: ______________
2.
Let $f(x) = x^{2} - 2x$ . Find the average rate of change of $f$ from $x = 1$ to $x = 4$ .
Answer: ______________
3.
A graph starts at $(-4, 2)$ , falls to a low point at $(-1, -3)$ , rises to a high point at $(2, 5)$ , then falls to its end at $(5, 0)$ . On which interval is the function increasing?
1. (A)
  $(-1, 2)$
2. (B)
  $(-4, -1)$
3. (C)
  $(2, 5)$
4. (D)
  $(-3, 5)$
4.
The table gives the height $h(t)$ , in metres, of a drone $t$ seconds after launch.

$t$ $0$ $2$ $5$
$h(t)$ $12$ $20$ $44$

What is the average rate of change of $h$ from $t = 2$ to $t = 5$ , in metres per second?
1. (A)
  $24$
2. (B)
  $8$
3. (C)
  $\dfrac{32}{3}$
4. (D)
  $6.4$
5.
What is the maximum value of the function $f(x) = -x^{2} + 6x - 5$ ?
Answer: ______________