Essential Skills Chapter 3
1.
Simplifying the difference quotient 
Section 3.1
Example: For 
, find 
and simplify
completely.
Answer: 
2. Finding the domain of a function Section 3.1
Example: Find the domain of 
.
Answer: 
3. Finding information from the graph of a function Sections 3.2 and 3.3
Example: The graph
of a quadratic function f is given
below. ItŐs vertex is at 
.
Use the graph to answer the following questions.
a.
On what interval is the function increasing? Answer: 
b.
On what interval is the function decreasing? Answer: 
c.
What is the domain of the function? Answer: 
d.
What is the range of the function? Answer: 
e. Which does this function have, a maximum or minimum value? What is it? Answer: A minimum value; 1
f.
Which of the following could be the formula for 
? Answer: iv
i. 
ii. 
iii. 
iv. 
4. Finding the average rate of change of a function Section 3.3
Example: Find the average rate of change of the
function 
on the invertval
.
Answer: 
5. Sketching graphs of basic functions Section 3.4
Example: Sketch the graph
of 
.
Answer: 
6. Sketching graphs of basic functions using transformations Section 3.5
Example: Sketch the graph of 
Answer: 
7. Constructing functions for modeling Section 3.6
Example: Consider the region in the plane
bounded by 
, x = 9 and the x-axis.
Each
value of x, 
, corresponds to an inscribed rectangle whose right side lies
along the line x = 9 (see figure). Write a function that expresses the area of the inscribed
rectangle as a function of x.
Answer: 