Introducing
Your new presentation assistant.
Refine, enhance, and tailor your content, source relevant images, and edit visuals quicker than ever before.
Trending searches
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.
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.
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
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
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 0<b<1 = horizontal stretch
If b>1 = horizontal shrink
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.
Example 2
Example 3
Example 1
- It determines the end behavior (based on largest coefficient)
- Knowing your largest coefficient (degree), use n-1
- Example: Degree is 5 = 5 -1 = 4 turning points
- If it is odd, it will have an opposite end behavior. (Up & down) (Down & up)
- If it is even, it will have the same end behavior (up & up) (down & down)
- It is the power of the root
- 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
- Your x-int and y-int are your other points