Alg. 1-2 DA

Unit 3Notes

Like pictures, graphs communicate a lot of information. So you need to be able to interpret, draw, and communicate about graphs. Most graphs you’ve seen represent functions – some of these graphs were lines, or linear, and others were curves or nonlinear(like exponentials).
Example 1 – This graph shows the depth of the water in a leaky swimming pool. Tell what quantities are varying and how they are related. Give possible real-world events in your explanation.

What is the domain? ______
What is the range? ______
Vocabulary
  1. A ______variable is a variable whose values depend on the values of another variable.
  1. An ______variable is a variable whose values affect the values of another variable.
  1. The input values are ______& the out values are ______.
  1. A function is ______when the x and y-values change in the same direction – that is, the y-values grow when the x-values grow. When reading the graph from left to right the graph goes uphill.
  1. A function is ______when the x and y-values change in different directions – that is, the y-values drop when the x-values grow. When reading the graph from left to right the graph goes downhill.
  1. ______functions have no breaks in the domain or range.
  1. ______functions’ domain and range are made up of distinct values rather than intervals of real numbers. Often looks like individual dots.
  1. When writing a rate such as miles per hour the units of measure are always dependent per independent.

Example 2 – Describe this graph, telling where the graph is increasing and where it is decreasing.

What is the domain?
What is the range?
Label where the graph is increasing and decreasing.
0 < x < 3
3 < x < 4.5
Label the independent and the dependent axis.
Find the following:
a. f(1.5) b. f(3) c. f(4.5)
d. x when f(x) = 1.5
Example 3 – For each scenario, identify the independent and dependent variables.
a. Benjamin is making T-shirts for a high school volleyball team. The press he runs can imprint 3 T-shirts per minute with the school’s mascot.
Independent: ______
Dependent: ______/ b. Gavin works for a skydiving company. Customers pay $200 per jump to skydive in tandem skydives with Gavin.
Independent: ______
Dependent: ______
c. Elizabeth is training for the Mini-Marathon. She is currently training at a pace of 3.75 miles per hour.
Independent: ______
Dependent: ______/ d. Nick is playing video games at the arcade. Nick starts with $20 and is playing games that cost $0.75 per game.
Independent: ______
Dependent: ______
e. Matt works for a laser tag company. Customers pay $11 per game of laser tag.
Independent: ______
Dependent: ______/ f. The higher the temperature in an oven the faster a cake will bake.
Independent: ______
Dependent: ______
Example 4
Find the domain and range. / Label the independent and the dependent axis.
Label where the graph is increasing and decreasing. / What would neither increasing nor decreasing look like in a graph?
Use the above graph to find the following.
a. f(4) / b. f(12) / c. f (18) + f (6)
d. f(16) / f(6) / e. f(20) – f(10) / f. f (10) ∙ f (4)
g. 5 ∙ f(9) / h. x when f(x) = 12 / i. x when f(x) = 8
j. x when f(x) = 0 / k. x when f(x) = 4 / l. x when f(x) = 16
Practice: Label the independent and dependent axes. Find the domain and range. Tell where the graph is increasing, decreasing and neither. Use the graph to find each function value listed below. Then do the indicated operations.

Domain:
Range:
Tell where the graph is increasing
and decreasing:
Find the independent and the dependent variable.
Independent:
Dependent:
a. f(2) / b. f(14) / c. f (8) + f (1)
d. f (16) / f (3) / e. f (20) – f (11) / f. f (0) ∙ f (-1)
g. f (-2) + f (13) – 3 / h. x when f(x) = 2 / i. x when f (x) = 14
j. x when f (x) = 10 / k. x when f (x) = 118 / l. x when f (x) = -1