WARM UP: a) Which of the following relations are also functions? Why? A B C

Vertical Line Test

Function Notation You've been playing with "y =" sorts of equations… Now that you’re grown up in Algebra 2…. In place of "y" use "f(x)" (pronounced as "eff-of-eks") You used to say "y = 2x + 3; solve for y when x = –1". Now you say "f(x) = 2x + 3; find f(–1)" (pronounced as "f-of-x is 2x plus three; find f-of-negative-one)

Function Notation Function notation gives you greater flexibility than using just "y" for every formula Your graphing calculator will list different functions as y1, y2, etc. In textbooks and when writing things out, we use names like f(x), g(x), h(x), s(t), etc.

Evaluating Functions Remember: Parentheses have, up until now, always indicated multiplication The parentheses do not indicate multiplication in function notation. The expression "f(x)" means "plug a value for x into a formula f " The expression does not mean "multiply f and x"! Don't embarrass yourself by pronouncing (or thinking of) "f(x)" as being "f times x". Given f(x) = x 2 + 2x – 1, find f(2).

WARM UP: Given f(x) = -2x 2 + 2x – 1, find f(3).

Remember Set Notation

Interval Notation

Is used when there is a open dot or the number is NOT included on the graph. Is used when there is a closed dot or when the number is included on the graph. Is used when one number is excluded.

Domain and Range: Graph

Special case: When there is an open circle and closed circle on the same number – go with the closed circle.

Domain and Range: Graph

Maximum or Minimum Point Max. Point – is the HIGHEST on the graph Min. Point – is the LOWEST on the graph

Maximum or Minimum Value? Where? Max. Point (0, 4)

Maximum or Minimum Value? Where? Min. Point (-1, -9)

ZEROS are the same thing as the X-INTERCEPTS.

Name the zeros. (-4, 0) and (3, 0)

Name the Y-INTERCEPT. (0, -4)

Interval of Increase, Interval of Decrease, & Constant Graphs To find where the graph is increasing and decreasing, trace the graph with your finger from left to right. Specify the x-values!

Increasing, Decreasing, & Constant: Graphs  If your finger is going up, the graph is increasing.  If your finger is going down, the graph is decreasing.  If your finger goes neither up or down…then the graph is CONSTANT.

The x-values where the graph is going down. Find the interval of decrease.

The x-values where the graph is going up. Find the interval of increase

Interval of increase: Interval of decrease:

Interval of increase: Interval of decrease: