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How is "combining functions" different from "composition of functions"?

Composition of functions is different than combining functions is because you are plugging "g" and "f" into each other by x rather than combining together.

Example

What is combining functions?

What is a function?

A function is a relation that has exactly one value for each range value (input & output)

Combining functions is when two functions of f and g are combined to form new functions.

Example

Function Mind

Map Project

What are quadratic functions?

What are the 3 different types?

The quadratic formula is any function of form f(x) = ax^2 + bx + c = 0.

Standard: ax^2 + bx + c = 0.

Intercept: f(x) = (x-p) (x-q)

Vertex: f(x) = a(x-h)^2 +k

By: Jennifer Phan

Amanda Wiley

Vertex: The highest/lowest point & where the parabola crosses its Axis of Symmetry

X-Intercept: Point that crosses x-axis. Set to zero and solve.

Y-Intercept: Point that crosses y-axis.

- Opens up if positive(min), & opens down if negative (max)

Transformations: How do you know where to move?

USE the equation f(x) = +/- af [+/-b (x +/- c)] +/- d

to determine where and how to move the function

Moving Left & Right

Vertical Stretch & Shrink

Horizontal Stretch & Shrink

From the equation(Slide 8), you would use (x +/- c) to determine whether it went left or right

From the equation (Slide 8), you would use (b).

From the equation (Slide 8), you would use (a)

If (x+c), it would move left

If (x-c), it would move right

If a>1 = Vertical stretch

If 0<a<1 = Vertical Shrink

If 0<b<1 = horizontal stretch

If b>1 = horizontal shrink

Example

What is the inverse?

How do you find the

inverse?

Reflection

If -f(x) = reflection is over the x-axis (change y-value sign)

If f(-x) = reflection is over the y-axis (change x-value sign)

The inverse is the opposite operation of a function.

It is when you switch the x and y. Then you solve for y. Your answer = Inverse.

Polynomials

Example 2

Example 3

Example 1

What is the coefficient test?

8 Types

of Functions

- It determines the end behavior (based on largest coefficient)

How do we know the number of turning points?

Polynomials Cont.

- Knowing your largest coefficient (degree), use n-1

Compare odd and even degree.

- Example: Degree is 5 = 5 -1 = 4 turning points

- If it is odd, it will have an opposite end behavior. (Up & down) (Down & up)

Multiplicity

- If it is even, it will have the same end behavior (up & up) (down & down)

- It is the power of the root

Compare positive & negative leading coefficient.

- If it is odd, it crosses the x-axis. If even, it bounces off.

- If the coefficient is positive, the polynomial goes up.

- If the coefficient is negative, the polynomial goes down

Zeros of Functions

- Your x-int and y-int are your other points

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