1. First blank: y-axis 2. Second blank: x-values 3. Third blank: y-values Filled sentence: Horizontal transformations reflect a function over the **y-axis**. Thus, they transform …
to review functions and their transformations, complete the following activity. drag and drop the words into the correct locations. horizontal transformations reflect a function over the. thus, they transform a given function $y = f(x)$ to $y = f(-x)$. to reflect a given function horizontally, multiply all by $-1$ while keeping the the same. $y$-values $x$-axis $y$-axis $x$-values
If the funtionnis f (x) =x3 complete thr table for its horizontal f election
The table has x on top then 0,1,2 then under that js f(-x) then 3 blank box’s HELO fill thoes in
The parabola rises and falls in a quadrant 4. The curve passes through left parentheses 0.4 comma negative 5 right parentheses left parentheses 1 comma negative 2 right parentheses peak at vertex left parentheses 2 comma 0 right parentheses descends through left parentheses 3 comma negative 2 right parentheses and left parentheses 3.6 comma negative 5 right parentheses all values are approximate. The table shows x -1, -2, -3 and under is f(-x) then 3 blank boxes help me fill thoes in
F(x)=(x+1)2 and the function of it’s horizontal reflection whag js the potion of the point (-4,9) in the reflected funtin the (-4,9) reflects to blank in f(-x)
If point (3,-5) is on the graph of f(x) what point must be on the graph of f(-x)
to review functions and their transformations, complete the following activity. drag and drop the words into the correct locations. horizontal transformations reflect a function over the. thus, they transform a given function $y = f(x)$ to $y = f(-x)$. to reflect a given function horizontally, multiply all by $-1$ while keeping the the same. $y$-values $x$-axis $y$-axis $x$-values
If the funtionnis f (x) =x3 complete thr table for its horizontal f election
The table has x on top then 0,1,2 then under that js f(-x) then 3 blank box’s HELO fill thoes in
The parabola rises and falls in a quadrant 4. The curve passes through left parentheses 0.4 comma negative 5 right parentheses left parentheses 1 comma negative 2 right parentheses peak at vertex left parentheses 2 comma 0 right parentheses descends through left parentheses 3 comma negative 2 right parentheses and left parentheses 3.6 comma negative 5 right parentheses all values are approximate. The table shows x -1, -2, -3 and under is f(-x) then 3 blank boxes help me fill thoes in
F(x)=(x+1)2 and the function of it’s horizontal reflection whag js the potion of the point (-4,9) in the reflected funtin the (-4,9) reflects to blank in f(-x)
If point (3,-5) is on the graph of f(x) what point must be on the graph of f(-x)
Filled sentence:
Horizontal transformations reflect a function over the y-axis. Thus, they transform a given function $y = f(x)$ to $y = f(-x)$. To reflect a given function horizontally, multiply all x-values by $-1$ while keeping the y-values the same.
Got it! First, let's remember that the horizontal reflection of \( f(x) = x^3 \) is \( g(x) = f(-x) = (-x)^3 = -x^3 \).
Let me make a sample table with common x-values to show both the original and reflected function values:
| x | Original \( f(x) = x^3 \) | Reflected \( g(x) = -x^3 \) |
|----|---------------------------|------------------------------|
| -2 | \( (-2)^3 = -8 \) | \( -(-2)^3 = 8 \) |
| -1 | \( (-1)^3 = -1 \) | \( -(-1)^3 = 1 \) |
| 0 | \( 0^3 = 0 \) | \( -0^3 = 0 \) |
| 1 | \( 1^3 = 1 \) | \( -1^3 = -1 \) |
| 2 | \( 2^3 = 8 \) | \( -2^3 = -8 \) |
See how each reflected y-value is just the opposite of the original? That’s the horizontal flip over the y-axis doing its thing. Did you have specific x-values you needed to fill in, or is this enough? 😊
Got you, let's fill those in quick!
Since the original function is \( f(x) = x^3 \), the horizontal reflection is \( f(-x) = (-x)^3 \). Let's calculate each one:
So the blanks under f(-x) are 0, -1, -8 in order! 😎
Got it, let's work through this step by step!
First, remember that f(-x) means we take each given x-value, flip its sign, then find the corresponding y-value from the parabola's points you described.
Let's go one by one:
To recap, the blanks (in order for x=-1, -2, -3) are: -2, 0, -2
Got it, let's break this down simply!
First, the horizontal reflection of \( F(x) = (x+1)^2 \) is \( F(-x) = (-x + 1)^2 \).
Now, to find where the…
Filled sentence:
Horizontal transformations reflect a function over the y-axis. Thus, they transform a given function $y = f(x)$ to $y = f(-x)$. To reflect a given function horizontally, multiply all x-values by $-1$ while keeping the y-values the same.
Got it! First, let's remember that the horizontal reflection of \( f(x) = x^3 \) is \( g(x) = f(-x) = (-x)^3 = -x^3 \).
Let me make a sample table with common x-values to show both the original and reflected function values:
| x | Original \( f(x) = x^3 \) | Reflected \( g(x) = -x^3 \) |
|----|---------------------------|------------------------------|
| -2 | \( (-2)^3 = -8 \) | \( -(-2)^3 = 8 \) |
| -1 | \( (-1)^3 = -1 \) | \( -(-1)^3 = 1 \) |
| 0 | \( 0^3 = 0 \) | \( -0^3 = 0 \) |
| 1 | \( 1^3 = 1 \) | \( -1^3 = -1 \) |
| 2 | \( 2^3 = 8 \) | \( -2^3 = -8 \) |
See how each reflected y-value is just the opposite of the original? That’s the horizontal flip over the y-axis doing its thing. Did you have specific x-values you needed to fill in, or is this enough? 😊
Got you, let's fill those in quick!
Since the original function is \( f(x) = x^3 \), the horizontal reflection is \( f(-x) = (-x)^3 \). Let's calculate each one:
So the blanks under f(-x) are 0, -1, -8 in order! 😎
Got it, let's work through this step by step!
First, remember that f(-x) means we take each given x-value, flip its sign, then find the corresponding y-value from the parabola's points you described.
Let's go one by one:
To recap, the blanks (in order for x=-1, -2, -3) are: -2, 0, -2
Got it, let's break this down simply!
First, the horizontal reflection of \( F(x) = (x+1)^2 \) is \( F(-x) = (-x + 1)^2 \).
Now, to find where the point (-4, 9) maps to on the reflected function:
When we do a horizontal reflection, we flip the sign of the original x-value (because we're replacing x with -x in the function). The y-value stays the same, since horizontal transformations don't affect the output.
Original x-coordinate: -4 → flipped x-coordinate is -(-4) = 4
Original y-coordinate: 9 → stays 9
Wait, let's double-check by plugging in to confirm: \( F(-4) = (-4 + 1)^2 = (-3)^2 = 9 \) (that's the original point). For the reflected function, plug x=4: \( F(-4) \) is the original, but the reflected function at x=4 is \( F(-(4)) = F(-4) = 9 \). Yep, that matches.
So (-4, 9) reflects to (4, 9) in \( f(-x) \)!
Got it, let's figure this out! A horizontal reflection (which is what f(-x) is) flips the x-coordinate's sign but keeps the y-coordinate the same.
Since (3, -5) is on f(x), we just flip the x-value from 3 to -3, and leave y as -5. So the point on f(-x) is (-3, -5)! 😊
If point (3,-5) is on the graph of f(x) what point must be on the graph of f(-x)
Top-left cell: 180 Top-right cell: 6 Bottom-left cell: 600 Bottom-right cell: 20 Final product: 806
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