Shrine of Functions Project by Connor Davidge https://padlet.com/connord23/1uic90uyhcbiz356 Algebra II en-us 2020-05-08 18:20:35 UTC 2026-04-19 22:47:25 UTC hello@padlet.com Assigned Functions armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/560493387 Armando Romero - Exponential
Connor Davidge - Rational
Henry Robertson - Radical
Harrison Limbaugh - Linear & Quadratic]]> 2020-05-08 18:29:52 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/560493387 Algebraic connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568318936 f(x) = p(x)/q(x)]]> 2020-05-12 18:06:52 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568318936 Linear Functions https://padlet.com/connord23/1uic90uyhcbiz356/wish/568323340 Verbal

Algebraic
y=mx+b
Numeric

Graphical

]]> 2020-05-12 18:08:42 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568323340 Quadratic Functions https://padlet.com/connord23/1uic90uyhcbiz356/wish/568324064 Verbal

Algebraic
y=ax^2+bx+c
Numeric

Graphic]]> 2020-05-12 18:09:01 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568324064 Numerical armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568377205 f(x)=3^x]]> 2020-05-12 18:32:00 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568377205 Linear Functions harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568377825 Verbal 
The input is the same as the output.
Algebraic 
y=mx+b
Numerical
(see below)
Graphic]]> 2020-05-12 18:32:18 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568377825 Verbal henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568386335 As the input increases the output also increases. This will go on to infinity. The y value is the square root of the x value. Because it is impossible to find the negative square root all x values must be positive. ]]> 2020-05-12 18:36:03 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568386335 Algebraic henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568387424 f(x)=a (sqrt b(x+c))+d]]> 2020-05-12 18:36:31 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568387424 Numerical henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568389319 2020-05-12 18:37:22 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568389319 Graphical henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568389907 2020-05-12 18:37:38 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568389907 Verbal connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568394423 As the input gets larger the output gets smaller and approaches 0. ]]> 2020-05-12 18:39:31 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568394423 Numerical connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568400149 f(x) = 1/x]]> 2020-05-12 18:41:58 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568400149 Graphical connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/568413370 f(x) = 1/x]]> 2020-05-12 18:47:57 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/568413370 Explanation connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575750132
If a rational function has the same factor on both the top and bottom, the graph will show a hole.
e.g. f(x) = (x+5)(x-3)/(x-3)

If you set the denominator to 0 you can find the vertical asymptotes
e.g. f(x) = 3x - 1/x - 5
x - 5 = 0
vertical asymptote is at 5

If the variable numerator and the denominator are both to the same degree, then divide the coefficients.
e.g. f(x) = 6x^2/2x^2
               = 6/2
Horizontal asymptote at y = 3

If the number in the numerator is a lower degree than the denominator, y = 0 is the horizontal asymptote.

If the number in the numerator has a higher degree than number in the denominator then there is no horizontal asymptote.

(Source)]]> 2020-05-15 18:06:19 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575750132 Behavior connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575750477 Domain: (-∞, 0) (0, ∞) 
Range: (-∞, 0) (0, ∞) 
End Behavior:
- As x → ∞, y → 0
- As x → -∞, y → 0
Common Transformations:
- Translations → y = 1/x +1
- Compressions → y = 0.5/x
- Stretches → y = 2/x
Inverse: For the parent function of  f(x) = 1/x the inverse is 1/x. However for more complicated functions the inverse may not be a function.

]]> 2020-05-15 18:06:29 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575750477 Graphical armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575752696 f(x)=3^x]]> 2020-05-15 18:07:39 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575752696 Linear Function's - Numerical harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575753267 2020-05-15 18:07:59 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575753267 Algebraic armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575757037 f(x)=ab^x

b:
- constant/change factor
- always positive 
- value raised to the x
a:
- starting/initial value/y-intercept
x:
- independent variable/input of the function]]> 2020-05-15 18:10:05 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575757037 Verbal armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575758050 As the input gets larger, the output gets larger and approaches ∞.]]> 2020-05-15 18:10:38 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575758050 Quadratic Functions harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575761089 Verbal 
y is porportional to the square of x
Algebraic
y=ax^2+bx+c
Graphic]]> 2020-05-15 18:11:49 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575761089 Behavior henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575761538 Domain: [0,∞)
Range: [0,∞)
End Behavior:
As x → ∞, y → ∞]]> 2020-05-15 18:11:57 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575761538 Behavior armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575769241 Domain: (- ∞, ∞)
Range: (0,  ∞)
End Behavior:
- As x→ ∞, y→ ∞
- As x→ -∞, y→ 0
Common Transformations:
- Translations→ y=3^(x)+2
- Compressions→ y=0.5(3)^x
- Stretches→ y=2(3)^x
- Inverse→ x=3^y


]]> 2020-05-15 18:15:51 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575769241 Something Interesting connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575775478 Rational functions can have holes which are single points in the graph that cannot exist. Holes are created when the input causes both the numerator and denominator to be equal to zero.]]> 2020-05-15 18:18:53 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575775478 Quadratic Function - Numeric harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/575782934 2020-05-15 18:22:46 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/575782934 Real-World Application connord23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/576189238 Rational Equations can be used to model multi-person work problems

Person 1 lays 500 bricks an hour
Person 2 lays 400 bricks an hour

How long working together will it take them to lay 1800 bricks?

By using two rational equations you can create a proportion allowing you solve for the unknown amount of time. In this example it is two hours

]]> 2020-05-16 00:06:38 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/576189238 Behavior- Linear Functions harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/581582550 Domain (-∞,∞)
Range (-∞,∞)
End Behavior
As x →∞, y→∞
As x→-∞, y→-∞]]> 2020-05-19 05:57:18 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/581582550 Something Interesting armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583197400 - Exponential functions are some of the most commonly used type of functions in real world scenarios. Populations are shown with exponential functions, investments are computed using exponential functions, and exponential functions are even used to carbon date artifacts (AlgebraLAB). ]]> 2020-05-19 18:11:06 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583197400 Real World application - Linear harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583209918 Linear can be applied to a lot of different things such as the distance you travel by car. X is distance and Y is time and it will go in a straight, linear fashion.]]> 2020-05-19 18:17:00 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583209918 Real World application- Quadratic harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583212832 Quadratic functions can be applied to the arch of a ball thrown through the air. The ball will arch resembling the quadratic function.]]> 2020-05-19 18:18:18 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583212832 Transformations henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583220763 This is the basic equation:
f(x)=a (sqrt b(x+c))+d

a creates a vertical stretch 2(sqrtx)
b creates a horizontal stretch (sqrt2x)
c creates a horizontal shift  (sqrtx+1)
d creates a vertical shift sqrtx)+1

The inverse:  The inverse is represented by x^2 . The inverse is also ((x-d)a)^2/b-c]]> 2020-05-19 18:21:54 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583220763 Explanation of Different "Representations" armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583235865 - The importance of "a" in an exponential function is that, exponential functions will always increase or decrease so they must have a starting value to know where to start decreasing or increasing.
- "b" is important in exponential functions because it's the value at which the function will either increase or decrease. Some may see this as the percentage that an equation changes by. "b" will always ]]> 2020-05-19 18:29:06 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583235865 Explanation henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583249176 The most important part of a radical function is the starting point of the function.
for the simple equation of sqrt of x the graph will start on the orgin and move to the right. "c" and "d" affect where the function starts "a and "b" determine the direction of the swoosh.]]> 2020-05-19 18:35:22 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583249176 Interesting facts - Linear harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/583986675 Linear function's slopes are shown in their equation. The slope is the number that directly modifies the x.]]> 2020-05-20 04:39:32 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/583986675 Behavior- Quadratic harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/584003139 Domain: (-∞,∞)
Range: [0,∞)
End Behavior:
As x approaches ∞ Y approaches ∞]]> 2020-05-20 04:59:50 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/584003139 Important Stuff - Quadratic harrisonl231_1 https://padlet.com/connord23/1uic90uyhcbiz356/wish/584008518 Quadratic Funtions]]> 2020-05-20 05:06:42 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/584008518 Real-World Application armandor23 https://padlet.com/connord23/1uic90uyhcbiz356/wish/584029640 Suppose $4000 is invested at a 6% interest rate compounded annually. How much money will there be in the bank at the end of five years? At the end of 20 years?

Assigned variables:
x= time in years and 
y= amount of money in investment account. 

y=4000⋅(1.06)^x

To find total amount of money after 20 years:

y=4000⋅(1.06)^20
]]> 2020-05-20 05:31:59 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/584029640 Something Interesting henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/586062802
There are many different types of radical functions. x under a cube root sign is also a radical function. This continues on forever. Because of this radical functions can look very different for example, cube root radicals go on forever in both directions, there is no starting point.

This means the final basic equation is a(b(x-c)^1/e-d. I didn't include this in earlier entries for simplicity. ]]> 2020-05-21 00:35:02 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/586062802 Real World Example henryr231 https://padlet.com/connord23/1uic90uyhcbiz356/wish/586071429
Radical functions are found everywhere. Rocket scientists and the simple Joes both use radical functions. This is because our world is built upon exponents and thusly radicals.

For example you have a square garden that has an area of 25 feet. How much fence in feet do you need to wrap the entire garden. The first step of this problem is to take the square root of 25 which is 5. Then you times 5 by 4 to get 20 feet of fence. 

Radical functions are also used in problems involving volume, gravity, and even plumbing. ]]> 2020-05-21 00:43:01 UTC https://padlet.com/connord23/1uic90uyhcbiz356/wish/586071429