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

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

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

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

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

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

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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.

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

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

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

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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.

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

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

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

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

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

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

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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

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

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

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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.

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

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

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

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

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

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

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Different notations effect the graph by rotation or translation.

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

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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

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

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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.

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

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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

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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

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

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

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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)

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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.

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even functions are vertically symmetrical and odd functions are diagonaly symmetrical

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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

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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

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neither=no symmetry

odd= symmetrical diagonal

even= vertically symmetrical

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

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

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

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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.

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

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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.

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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

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

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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

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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

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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).

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

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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.

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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.

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

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

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

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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).