Activity 0.1 Functions

Activity 0.1 Functions

Name:

ID:

Date:

Part I. Function Evaluation

1.
Let $f(x) = 3x^2 - 4x + 2$. Evaluate the following:
a) $f(-2)$
b) $f(0)$
c) $f(a+1)$
2.
Given $g(t) = \displaystyle \frac{\sqrt{t+4}}{t}$, evaluate $g(5)$.

Part II. Domain and Range

3.
Find the domain of the function $h(x) = \displaystyle \frac{x-1}{x^2 - 9}$. Write your answer in interval notation.
4.
Find the domain of $p(x) = \sqrt{10 - 2x}$.
5.
State the domain and the range of the function $f(x) = x^2 - 4$.

Part III. Conceptual Understanding

6.
Which of the following sets of ordered pairs represents a function? Circle the correct option.
- a) $\{(1, 2), (2, 3), (1, 4), (5, 6)\}$
- b) $\{(0, -1), (2, -1), (4, -1), (6, -1)\}$
- c) $\{(3, 3), (3, 4), (3, 5), (3, 6)\}$
- d) $\{(-1, 0), (-1, 2), (0, 2), (1, 3)\}$
7.
Explain in your own words why a circle drawn on a Cartesian plane does not represent a function $y = f(x)$. Mention a specific test you can use.

Part IV. Graphical Analysis

8.

Determine the domain and range of the function shown in the graph below.
(Assume the curve continues infinitely upwards).
Domain: ____________________

Range: ____________________
9.

State the domain and range of the piecewise function plotted below.
(Pay attention to open and closed dots).
Domain: ____________________

Range: ____________________
10.
Which of the following functions corresponds to the graph shown on the right?
(Hint: Look at the vertex and the orientation).
- a) $f(x) = |x - 2| + 3$
- b) $f(x) = -|x + 2| + 3$
- c) $f(x) = -|x - 2| + 3$
- d) $f(x) = -|x - 3| + 2$