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yo les gars

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What are the differences between different types of functions?

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What are the differences between different types of functions?

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Linear Function - This type of function has a constant rate of change between the x and y values. It has a steady rate, therefore, when represented in graphs, it's always a straight line and not curved.

Exponential Function - This type of function's y values will drastically get greater/smaller as the y values have common ratio instead of a common difference like the linear functions have. An exponential graph never passes the horizontal asymptote; the horizontal asymptote depends on the graph. Meaning, an exponential function can be graphed as accelerating as the y values are drastically increased as the x values increases. So, it's curved rather than straight.

Quadratic Function - This type of function's always changes in sign of slope after the vertex. It can be also noted that it gets increasingly smaller when getting nearer to the vertex and after the vertex, it changes it signs. So, it's shaped like a U(parabola) rather than a straight line.

-Myra

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Regression predicts the estimation between the two variables, independent and the dependent variable.

The regression is often indicated as R^2 and the closer your regression, the more fit your function/table is to the specific function.

-Myra

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Figure out how to find the width of a rectangle using Pythagorean Theorem.

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To rotate it 180 degrees, you need to change the points from (x, y) to (-x, -y).

Change the Points (-1, 2) to (1, -2).

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To reduce the size by 1/2, we need to multiply 1/2 to each coordinate points.

A. (-4, -6)*1/2 = (-2, -3)

B. (0, -6)*1/2 = (0, -3)

C. (0, -10)*1/2 = (0, -5)

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How do you know which type of function fits an equation/function?

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How do you know which type of function fits an equation/function?

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In Functions and Statistics, we learned about regression. In this part, we mainly used desmos. However, we had to learn the different equations for functions.

-Myra

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Then, type in your values into a table in Desmos

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A straight line is linear

A big curve is exponential

A circular V looking thing means quadratic

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Red: Vocabulary
Blue: Notebook Work/Schoolwork
Purple: How to solve

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Descriptions: Red
Photos: Blue
IXL: Black
Videos: Purple

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Purple: Videos and images
Orange: Facts and tips
Blue: Links
Green: Sample Problems

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Pythagorean Theorem (hypotenuse and legs)

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Pythagorean Theorem (hypotenuse and legs)

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1. Rotation:

90 clockwise - (x, y) to (y, -x)

90 counterclockwise - (x, y) to (-y, x)

180 clockwise and counterclockwise - (x, y) to (-x, -y)

270 clockwise - (x, y) to (-y, x)

270 counterclockwise - (x, y) to (y, -x).

2. Translation:

If you want to move a units up or down, you need to add or subtract that from y.

If you want to move a units left or right, you need to add or subtract that from x.

For example, if you want to move 2 units up and 5 units right, the new coordinates must look like this : (x+5, y+2)

3. Dilation:

Multiply x and y by the amount you want to increase.

For example, if you want to increase the size twice, multiply both x and y by 2.

4. Reflection:

x-axis - (x, y) to (-y, x)

y-axis - (x, y) to (y, -x)

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What's the Difference Between Expressions and Equations?

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Algebra Basics: Solving Basic Equations Part 2 - Math Antics

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https://youtu.be/QEnFIgN8UBw

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Translating Words To Algebraic Expressions Explained!

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This will make rotations easier
https://youtu.be/tdWrAzE8r3U

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Algebra Basics: Solving 2-Step Equations - Math Antics

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An example of expression

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Rise over run

-Rise means how many units you move on the graph up or down. Run means when you move the unit to left or right, those  are x values.The slope of a line is often stated as a fraction known as rise over run.

-Clori

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Description of Equation
An equation is a mathematical statement that consists of two sides separated by an equals (=) sign. Equations are used to represent balance or equivalence between two quantities. The solution to an equation is the value of the variable that make both sides of the equation equal.

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Step by step on finding a matching equation and table using only a graph for a linear function.

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Step by step on finding a matching equation and table using only a graph for a linear function.

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1. Find out what you know by looking at the graph
Is it inclined to the right (Positive)? Is it inclined to the left
(Negative)? What's the y-intercept?

2. Find the rate of change (ROC) by using the following formula     y2 - y1 / x2 - x1.

3. Use the pair from x1 and y1 OR x2 and y2 in order to check if   the equation is working or not

4. Using the points from before find out the table by using the rate of change on them.

5. Now check the table, by putting the numbers from the table into the equation from before!

Jeff

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https://www.ixl.com/math/level-j/identify-reflections-rotations-and-translations

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IXL | Identify reflections, rotations, and translations | Level J math

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Improve your math knowledge with free questions in "Identify reflections, rotations, and translations" and thousands of other math skills.

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https://www.youtube.com/watch?v=l3XzepN03KQ

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Algebra Basics: Solving Basic Equations Part 1 - Math Antics

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https://youtu.be/BCllaARDOWI dilation done right

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Sample Problem 1-Translation and Reflection:

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Sample Problem 1-Translation and Reflection:

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Step 1: Move the triangle 15 units down. For example, the translated point b must be in -10 instead of 5 because 5-15 = 10. (15 units down.)
Step 2: To reflect it across the y axis, the new points' x values must be opposite. For example, the reflected point b must be 7 instead of -7

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https://www.youtube.com/watch?v=VJTxv-tRKj0

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3 Types of Transformations *Translations Reflections & Rotations *Math For Kids*

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the different transformations consists of first transition, when the shape moves to another point on the grid. Rotation, when the shape goes either 90 degrees clockwise or counter clock wise. Reflection, when the shape reflects and basically becomes opposite of what it used to be for example if it’s across the X axis it goes from top to bottom or bottom to top and if it’s across the Y axis it’s goes from left to right or right to left. As for dilation it becomes smaller or larger by a certain amount it’s like if you scaled a imagine on your computer.

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Finding the missing side of a right triangle

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Finding the missing side of a right triangle

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Vocabs

Variable - a letter or a symbol used to represent a value that can change.

Numeric expressions - contains only constants and operations.

Algebraic expressions - contain variables, constants, and operations.

Constant - a value that does not change.

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Yes

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Dilation is a transformation, which is used to resize the object. Dilation is to make the object/shape smaller or bigger.

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For Dilation:
If the scale factor were to be between 0 to 1, the image shrinks.
If the scale factor were to be more than 1, then the image would stretch.
If it’s exactly 1, the image’s original size stays the same.

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Example problems; Finding out whether it is a right triangle off of the measurements for a, b, and c.

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Example problems; Finding out whether it is a right triangle off of the measurements for a, b, and c.

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- shwe yi

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An example of an expression

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Blue = Vocabulary
Green = Notes
Purple = Examples
Black = Tips/Fun Facts

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Divide a by 4-
a/4

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For Rotation:

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

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If it's a graph check to see if it passes the vertical line test.

If it's a table see if any x values repeat.

If it's an equation see if it follows the formats in "Equations"

Jeff

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Transformations in the plane can change the size, shape or position of a figure to create a new image.

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https://www.youtube.com/watch?v=GqHWdTLL8Qw

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Translations Reflections and Rotations - Geometric Transformations!

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- cindy

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Linear Function Equation: y = mx + b
Quadratic Function Equation: y = ax^2
Exponential Function Equation: y = a(b)^x

Jeff

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Translation - How much up or down does a shape move?
Rotation - How much does a shape rotate?
Reflection - Does a shape flip vertically or horizontally?
Dilation - By how much did a shape change in size?

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1. rotation
2. reflection
3. dilation
4. translation.

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Rotation

a shape is turned clockwise or counterclockwise around a given point

Reflection

a shape is flipped to create a mirror or congruent image

Translation

takes each point in a figure and slides it the same distance in the same direction

Dilation

changes the size of a shape to become either larger or smaller

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The 4 transformations include rotation, translation, reflection and Dilation.

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Interpreting expressions that represent quantities.
Terms, Factors, Coefficients.

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sum of the area of the triangle.
on the legs (a and b) equals the area of the square on the hypotenuse (c).
- cindy

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Finding the hypotenuse or leg of a right triangle
- shwe yi

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a2+b2=c2