Relations & Functions
Definition of a Function
A relation in which the x values do not repeat?
Absolute value of x means the distance from ____ to x
Zero
Define a system of equations.
A group or set of equations.
Shape that quadratic equations make when graphed.
Parabola, "u" shape.
The total of all the interior angles of a triangle.
180 degrees.
Consider relation S = {(1,2), (2,4),(?,6)}, state a value for ? will make S not a function.
1 or 2
Name something that an absolute value will never be.
Negative
Information that the intersection of two functions tell.
Solutions
The most important part/point of a parabola.
Vertex/Turning Point
A lake has a patch of lily pads. Every day, the patch doubles in size. If it takes 48 days for the patch to cover the entire lake, how long will it take for the patch to cover half of the lake?
47 days
Method to graphically verify if a relation is a function.
Vertical Line Test
Shape of an absolute value function graph.
"v" shape
Main methods to solve a system of equations.
- elimination
- substitution
- graphing
In the quadratic formula, what is the expression inside the radical term called?
The discriminant
True or false? A concave shape curves outwards.
False.
Find the range of x2+2.
[2,inf)
-|-(-3)2|
-9
Describe the system:
y=4x-9
y=x-3
Consistent, independent
Why, when taking square root of numbers, we must consider both the negative and positive values? For example, why is sqrt(4) = 2 and -2?
Because squaring negative numbers also gives a positive result (negative times a negative make a positive).
You have ten grey socks and ten blue socks you want to put into pairs. All socks are exactly the same except for their color. If you are in the dark and so can’t see, how many socks would you need to take out to ensure you have at least a pair?
3
Consider functions h(x) and j(x), if h(j(x))=x and j((h(x))=x, then what is true about h(x) and j(x)?
h(x) and j(x) are inverses of each other.
Explain: why does any horizontal shift take the opposite effect/direction?
Because whatever we find inside the absolute value function ex: |x-c| needs to be set equal to zero in order to solve for the factor of horizontal translation.
x-c=0, x=c, so it will move c units to the right (positive).
Consider the general system of equations.
a1x+b1y+c=0
a2x+b2y+c=0
State the description of the system if a1/a2 = b1/b2.
The system will be inconsistent.
(1) Name at least three real world scenarios that can be modeled using quadratic functions. (2) Concept that helps us determine whether a given tabulated set of values fit the model of a quadratic equation.
- Throwing a basketball
- Projectile motion
- Free fall
- Path of a roller coaster.
(2) Quadratic Regression
A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
5 cents.