Name_________________________________________
Ms. Hindal
Unit 1 Day 2
Pre-Calculus Honors
Objective 1.2: Interval Notation
Do Now:
1. If h(x) = 2x2 - 3, what is x when h(x) = 15
2. g(3 + 2) - 2 =
3. If f(x) – 3 = 2, find x
Interval Notation
All numbers from 3 to 10…
If it is _____________________ then 3 and 10 would be
included
If it is ________________________ then 3 and 10 are not
included (they are excluded)
Inclusive is…
Exclusive is…
Examples:
1. Inequality: 3 < x < 10
2. Inequality: 3 < x < 10
Interval Notation:
Interval Notation:
3. Inequality: -4 < x < 2
NOTE:
Interval Notation:
Fill in the missing information
4. Inequality:
5. Inequality:
Interval Notation: (-1, 4]
Interval Notation:
Bounded vs. Unbounded
Unions
Inequality: x ≥ -2
Example: x < -1 OR 2 ≤ x
Interval notation:
Interval notation:
Name_________________________________________
Fill in the missing information
2. Inequality:
1. Inequality: -5 ≤ x < -4 OR -3 ≤ x
Interval notation: (-∞, 4)
Interval notation:
3. Inequality:
Interval notation:
Scratch Work:
Homework:
Write as an inequality and in interval notation.
1.
Write the following inequalities as interval notation:
3. -2 < x < 1 or x > 1
4. x < -3 or x > 3
2.
Pre-Calculus Honors
Objective 1.1 and 1.3: Function Notation Practice and Intro to Vocab
Function Notation Practice:
g(x) = 2x4 + x2
h(x) = x3 – 2x2
g(-x) =
h(-x) =
-g(x) =
-h(x) =
Name_________________________________________
Ms. Hindal
Exploration
Explore:
Mathematicians define an even function as one where f(-x) = f(x) for all values of x
An odd function is one where f(-x) = -f(x) for all values of x
A function can also be neither even nor odd.
We are going to explore characteristics of even and odd functions to help us practice our function notation.
1.
Is the function g(x) (in the function notation section above) even? This is the same as asking (based on our definition
of even above): does g(-x) = g(x)? Use what we have already done!
2.
Look at function h(x) in the function notation section above
a. Is the function h(x) even?
b.
3.
Let f(x) = –3x3. For the two parts it will help to find f(-x) and –f(x).
a. Is f(x) even?
b.
4.
Is the function h(x) odd (use the definition!!)?
Is f(x) odd?
Look at the graph describing the function B(x) below. We are going to determine if this function is even.
A function is even when: __________________________________________ (look above)
Let’s pick values of x to see if this is true.
a.
b.
c.
If x = 3, B(x) =
If x = 3, B(-x) =
When x = 3, does B(x) = B(-x)?
d.
When x = 5, does B(x) = B(-x)?
e.
Is this function even? (Remember, the statement has to be true for all x)
f.
Let’s assume B(x) is even. If that is the case, and the point (-12, -4) is a point on B(x), what also has to be a
point on B(x)? Think about what the graph would look like!
g.
If the point (x, y) were on the graph of the function, what other point would also be listed?
h.
Challenge: Write in words what the graph of an even function will look like. Why will it look this way?
5.
Name_________________________________________
Look at the graph describing the function D(x) below. We are going to determine if this function is odd.
A function is odd when: __________________________________________ (look above)
Let’s pick values of x to see if this is true.
a.
b.
c.
d.
If x = 4, D(-x) =
If x = 4, -D(x) =
When x = 4, does D(-x) = -D(x)?
When x = 6, does D(-x) = -D(x)?
e.
Is this function odd? (Remember, the statement has to be true for all x)
f.
Let’s assume D(x) is odd. If that is the case, and the point (-12, 3) is a point on D(x), what also has to be a point
on D(x)?
g.
If the point (x, y) is on the graph of an odd function, what other point will be on the graph?
h.
Challenge: Write in words what the graph of an odd function will look like. Why will it look this way?
6.
Is T(x), below, even, odd, neither, or both?
8.
Write out a table of values based on the points on the graph in question 5. What does the table of an odd function look
like?
-
7.
Write out a table of values based on the points on
the graph in question 4. What does the table of an
even function look like?