Period 7 2.2.3 by Kristen Ritter

Math- Cooper Edmundson

2024-10-10 16:23:20 UTC

by changing or adding on to f(x) in a table, it can translate, reflect, and transform the graph.

Math

drogers27_2 — 2024-10-10 16:24:41 UTC

Without knowing the equation, we can use the table to see how the graph will affected when f(x) is changed

2024-10-10 16:24:46 UTC

it helps show how x and y change based on the equation

vshebuski27 — 2024-10-10 16:25:19 UTC

Adding stuff or changing things in the F(x) on a table can translate or reflect on a graph.

Math

2024-10-10 16:25:19 UTC

In a radical if you add in a negative or 2 negatives to it, then it changes which quadrant the line is in.

Notation

2024-10-10 16:26:04 UTC

This is helpful because you can see how the graph will change without having to plug in numbers to the equation

Notation

2024-10-10 16:26:04 UTC

Instead of having to change the equation, you can instead just change the x and y values in the table to translate, reflect, and dilate the graph without actually graphing it.

Math

drogers27_2 — 2024-10-10 16:26:21 UTC

f(-x) horizontally flips the parent graph and -f(x) vertically flips the parent graph

Notation

2024-10-10 16:26:21 UTC

By making the h or k values negative, we can alter the position of the equation on the graph.

Math

2024-10-10 16:26:54 UTC

In a radical if you add in a negative or 2 negatives to it, then it changes which quadrant the line is in.

Notation

2024-10-10 16:27:14 UTC

In a table, some variables will only change the x-value column like h, but some will only change the y-value column like k.

vshebuski27 — 2024-10-10 16:27:24 UTC

-f(x) flips across the x axis and f(-x) flips it across the y axis.

2024-10-10 16:27:33 UTC

By altering x we can translate, reflect the graph without the equation.

Notation

mriggins28 — 2024-10-10 16:27:44 UTC

A notation shows how a graph will change based on how its f(x) is changed.

2024-10-10 16:27:48 UTC

-f(x) flips the graph across the x axis and f(-x) flips across the y axis

2024-10-10 16:27:53 UTC

By adapting f(x) by adding negatives and/or other numbers, transformations can occur, such as translations or dialations.

2024-10-10 16:28:01 UTC

changing f(x) can reflect and transform graph without changing the equation

Math

drogers27_2 — 2024-10-10 16:28:34 UTC

Even functions - the parent graph looks the same as horizontally reflected graphed

Odd functions - the vertically reflected graph looks the same as horizontally reflected graphed

Neither - no reflection looks the same

-f(x) vs f(-x)

2024-10-10 16:28:40 UTC

In a radical function, f(-x) is a horizontal reflection, if it's -f(x) is a vertical reflection.

2024-10-10 16:29:05 UTC

by adding negatives it flips the graph changing what quadrant it is in moving over the x and y axis

2024-10-10 16:29:08 UTC

In a radical function -f(x) creates a vertical reflection across the x-axis while f(-x) creates a horizontal reflection across the y-axis.

Math

2024-10-10 16:29:09 UTC

In odd functions x^4 and x^3 can appear the same if the h and k are similar.

-f(x) vs f(-x)

2024-10-10 16:29:30 UTC

-f(x)- would make it so that the graph is flipped horizontally

f(-x)- would make it so that the graph is flipped vertically

2024-10-10 16:29:43 UTC

-f(x) can vertically flip graphs over the center, while f(-x) can horizontally flip graphs over the center

mriggins28 — 2024-10-10 16:29:56 UTC

-f(x) reflects the graph across the x axis and f(-x) reflects the graph across the y axis.

2024-10-10 16:29:56 UTC

F(-x) horizontally flips the parent graph, whereas -f(x) vertically flips the parent graph.

2024-10-10 16:30:09 UTC

Different notations effect the graph by rotation or translation.

2024-10-10 16:30:11 UTC

The table shows how each coordinate pair is affected on the graph when you change f(x)

2024-10-10 16:30:14 UTC

horizontal reflection is when we reflect the graph across the y axis and vertical reflection is when we reflect the graph across the x axis

2024-10-10 16:30:24 UTC

odd and even both look the same as the reflected graph and neither dosemt look the same

Notation

2024-10-10 16:30:33 UTC

Function tables can be altered to fit a situation without making a new equation or re-multiplying the x-values, as different types of functions all stem from their respective parent functions and can easily be changed from this.

Math

2024-10-10 16:30:38 UTC

A negative inside the radical reflects the function horizontally while a negative outside ethe radical reflects the function vertically.

If a number is added or subtracted from "x" the f(x) either positive or negative, but when the -f(x) is the function the "y" coordinate changes

2024-10-10 16:30:53 UTC

2024-10-10 16:31:10 UTC

-f(x) has a vertical reflection, but f(-x) has a horizontal reflection.

2024-10-10 16:31:38 UTC

The f(-x) flips the graph horizontally and the -f(x) flips the graph vertically.

2024-10-10 16:31:59 UTC

Even functions are symmetrical so putting a negative for the x value doesn't change it; in odd functions there are the graph is laid out so that -f(x)=f(-x)

2024-10-10 16:32:12 UTC

Inclusion of different values, including negatives (reflections), h-values (translations along the x-axis), k-values (translations along the y-axis), and a-values (dilations and reflections) result in transformations of functions.

2024-10-10 16:32:23 UTC

even functions are vertically symmetrical and odd functions are diagonaly symmetrical

Odd/even/neither

2024-10-10 16:32:29 UTC

For even functions they have a line of symmetry across the y-axis while odd functions have a line of symmetry that is diagonal, if it is neither odd or even then there is no line of symmetry

2024-10-10 16:32:47 UTC

Even functions are symmetrical, and have f(x)=f(-x), while odd functions are asymmetrical and can be reflected horizontally, and have -f(x)=f(-x). y equals radical x is neither and can be flipped horizontally and vertically

vshebuski27 — 2024-10-10 16:32:55 UTC

neither=no symmetry

odd= symmetrical diagonal

even= vertically symmetrical

Negative radical has a horizonal reflection and when the negative is outside the radical it is a vertical reflection

2024-10-10 16:32:56 UTC

2024-10-10 16:32:58 UTC

Even functions have reflective symmetry, while odd functions have rotational symmetry. Neither has no symmetry

Odd/Even/Neither

2024-10-10 16:33:08 UTC

Even functions are symmetrical, so their reflections are the same, an odd function reflects the same way regardless of if f or x is negative because they are already reflected, some functions (like radical) are neither where none of their reflections are equal.

mriggins28 — 2024-10-10 16:33:25 UTC

Even graphs look the same over the y-axis, odd graphs look the same over the x-axis. Neither are not symmetrical at all.

2024-10-10 16:34:29 UTC

Even functions, including quadratic and absolute value, mean that the parent function looks the same when horizontally flipped, whereas odd functions look the same when vertically flipped. If it doesn't do either of these things, it is categorized as neither.

2024-10-10 16:34:34 UTC

Even functions are vertically symmetrical and typically use the functions x^2 and absolute values. The odd functions are diagonally symmetrical and uses cubic and rational functions

2024-10-10 16:34:52 UTC

even functions are horizontally symmetrical and the vertical reflection is diagonally symmetrical.

Even function is when the graph is equal on both sides, but when it is odd the graph takes up adjacent quadrants and a radical is neither if it only crosses one quadrant

2024-10-10 16:34:53 UTC

2024-10-10 16:35:20 UTC

Using a radical function (f(x)=√x), we can see how the use of negatives affects a function, including: f(x)=√(-x) (reflection across the y-axis), f(x)=-√x (reflection across the x-axis), and f(x)=-√(-x) (180° rotation about the origin).

2024-10-10 16:36:27 UTC

even functions are vertically symmetrical but odd functions are horizontally symmetrical.

2024-10-10 16:36:38 UTC

Even functions (including parabolas and absolute value functions) have f(x)=f(-x), while odd functions (including cubic and rational functions) display -f(x)=f(-x); functions including that of radical functions are neither even nor odd.

Math

2024-10-10 16:37:11 UTC

Even functions are the same when horizontally reflected, Odd functions are the same when a becomes negative and when it reflects vertically, and neither is when it's not the same.

2024-10-10 16:37:19 UTC

f(-x) flips left and right, -f(x) flips up and down

-f(x) vs f(-x)

2024-10-10 16:38:19 UTC

-f(x) causes a horizontal reflection over the x-axis, while f(-x) causes a vertical reflection over the y-axis.

2024-10-10 16:38:34 UTC

changing f(x) can transform the graph in diff ways.

Odd/Even/Neither

2024-10-11 19:29:52 UTC

Even functions are where f(x)=f(-x), odd functions are where f-(x)=f(-x), and functions that are neither do not follow any of these rules (they are a little bit wonky sometimes).