9/22/09

1

Algebra 2 1.7 – “Function” Notation

Not going to spend a lot of time on this because it’s SO SIMILAR to stuff you’re already familiar with.

Mainly introducing some new vocab related to “Function Notation”

Old vocab Recent Vocab New Vocab

X-value Input (Domain) Independent Variable

Y-value Output (Range) Dependent Variable

Here’s a question you’re�familiar with:

“Evaluate y = 2x – 5, when x = 4, 6, 8 and 10.”

Input Formula Output

X 2x – 5 y

4 2(4) – 5 3

6 2(6) – 5 7

8 2(8) – 5 11

10 2(10) – 5 15

9/22/09

2

Here’s the same question in “Function Notation”:

“Evaluate f(x) = 2x – 5, when x = 4, 6, 8 and 10.”

Indep. Var. Function f(x)

X 2x – 5 y

4 2(4) – 5 3

6 2(6) – 5 7

8 2(8) – 5 11

10 2(10) – 5 15

The character f(x) is read as �“The function of x…”

A FUNCTION is an algebraic expression (ex. 7 – 2x ) that shows how an input value (x) is manipulated mathematically to arrive at its unique output value

Ex. “If f(x) = 7 – 2x, evaluate f(0), f(1/2) and f(-2)”

Solution: Input (x) Function (7 - 2x) Output f(x)

0 7 – 2(0) 7

1/2 7 – 2(1/2) 6

-2 7 – 2(-2) 11

9/22/09

3

Examples: If f(x) = 3x2 – x + 2, evaluate f(0), f(1.5), f(-4)

  If this is a graph of f(x), evaluate f(-4), f(-1), f(0) and f(4)

9/22/09

4

  Graph the function g(x) = -2x + 4

p.55 #22 Scuba Diving “In order to scuba dive safely, divers must be aware that

water pressure is a function of depth. The water pressure increases by 0.445 pounds per square inch (psi) for each foot of depth. The pressure at the surface is 14.7 psi.”

1.  Write a function to represent Water Pressure.

2.  What is the value of the function for an input of 50?

3.  What does that represent?

4.  Prepare a function table of psi to a depth of 100 feet in 10’ increments.

5.  Graph your results.

9/22/09

5

1.  f(x) = (x – 1)2 + 4 Evaluate for the replacement set {-1, -1/2, 0, 1, 3}

2.  Graph the function of the replacement set

3.  How do we know by looking at it that this IS a “function”?