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Ella draws a hexagon on the coordinate grid and shifts it 7 units to the left. Use a function to show the translation. What function does Ella write?(1 point) Responses g(y)=y−7 g left parenthesis y right parenthesis equals y minuus 7 f(x)=x−7 f left parenthesis x right parenthesis equals x minus 7 f(x)=x f left parenthesis x right parenthesis equals x f(x)=x+7

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To represent the translation of a figure (in this case, a hexagon) 7 units to the left on a coordinate grid, we need to consider how the coordinates of the points of the shape will change.

A translation to the left involves subtracting from the x-coordinate of each point. This can be represented by a function where the output depends on the input variable \(x\) shifted to the left:

\[ f(x) = x - 7 \]

This function means that for each \(x\)-coordinate of the hexagon, you subtract 7 to get the new \(x\)-coordinate after the translation.

Thus, the correct function that Ella writes for the translation of the hexagon 7 units to the left is:

f(x) = x - 7

Ella draws a hexagon on the coordinate grid and shifts it 7 units to the left. Use a function to show the translation. What function does Ella write?(1 point) Responses g(y)=y−7 g left parenthesis y right parenthesis equals y minuus 7 f(x)=x−7 f left parenthesis x right parenthesis equals x minus 7 f(x)=x f left parenthesis x right parenthesis equals x f(x)=x+7

To represent the translation of a figure (in this case, a hexagon) 7 units to the left on a coordinate grid, we need to adjust the x-coordinates of all points.

The translation to the left is done by subtracting from the x-coordinate, so the correct function to represent this translation is:

f(x) = x - 7

This function signifies that for every x-coordinate, you perform the operation \(x - 7\), resulting in the shape being shifted 7 units to the left.

Therefore, the answer is:

f(x) = x - 7

Jaydin draws a triangle on the coordinate grid. Its vertices are at (−4,3) , (−1,−5) , and (−2,6) . He translates this triangle 5 units up and 2 units to the right. What are the coordinates of the lowest vertex on the translated triangle?(1 point) Responses (1,0) left parenthesis 1 comma 0 right parenthesis (−2,8) left parenthesis negative 2 comma 8 right parenthesis (4,−3) left parenthesis 4 comma negative 3 right parenthesis (0,1)

To find the coordinates of the lowest vertex of the triangle after translating it 5 units up and 2 units to the right, we first need to identify the lowest vertex of the original triangle.

The original vertices of the triangle are:

  • \( (-4, 3) \)
  • \( (-1, -5) \)
  • \( (-2, 6) \)

Among these, the lowest vertex is \( (-1, -5) \) because it has the lowest y-coordinate.

Now we will apply the translations:

  1. Translate 5 units up: This means we add 5 to the y-coordinate. \[ y = -5 + 5 = 0 \]

  2. Translate 2 units to the right: This means we add 2 to the x-coordinate. \[ x = -1 + 2 = 1 \]

After applying both translations, the coordinates of the lowest vertex on the translated triangle are:

\[ (1, 0) \]

So the answer is:

(1, 0)

A point is translated on the coordinate plane from (2,−5) to (2,−6). Create a function to show this translation. Which function shows the appropriate translation?(1 point) Responses g(y)=y g left parenthesis y right parenthesis equals y f(x)=x−1 f left parenthesis x right parenthesis equals x minus 1 g(y)=y−1 g left parenthesis y right parenthesis equals y minus 1 g(y)=y+1

To analyze the translation of the point from \((2, -5)\) to \((2, -6)\), we can observe that the x-coordinate remains unchanged (it stays at 2), while the y-coordinate decreases by 1 (from \(-5\) to \(-6\)).

To create a function that shows this translation, we can describe how the y-coordinate changes. The function indicates that for a given y-value, we subtract 1 to get the new y-value:

\[ g(y) = y - 1 \]

This function correctly represents the change in the y-coordinate while leaving the x-coordinate constant.

Therefore, the correct function that shows the translation is:

g(y) = y - 1

Mel draws triangle ABC and translates it along the coordinate grid to produce triangle A′B′C′ . Then, he determines the functions f(x)=x+h and g(y)=y+k that describe the translation. What are the values of h and k in these functions? (1 point) Responses h=−1 and k=−6 h equals negative 1 and k equals negative 6 h=6 and k=−1 h equals 6 and k equals negative 1 h=1 and k=6 h equals 1 and k equals 6 h=−1 and k=6

To determine the values of \(h\) and \(k\) in the functions \(f(x) = x + h\) and \(g(y) = y + k\), we need to understand how translations affect the coordinates of the points.

  1. The function \(f(x) = x + h\) translates the x-coordinates. If \(h\) is positive, the triangle moves to the right; if \(h\) is negative, it moves to the left.

  2. The function \(g(y) = y + k\) translates the y-coordinates. If \(k\) is positive, the triangle moves up; if \(k\) is negative, it moves down.

To find the values of \(h\) and \(k\), we need to know the original coordinates of the vertices of triangle ABC and their corresponding translated coordinates in triangle A′B′C′. However, based on the provided options, I can deduce the possible translations:

  • If \(h = -1\), the triangle moves 1 unit to the left.
  • If \(k = -6\), the triangle moves 6 units down.

Thus, if that matches the translation you have in mind, the values could be:

h = -1 and k = -6

If you have specific translations or vertex coordinates for triangles ABC and A′B′C′ that you can share, I could provide a more precise evaluation. But based on the options provided and standard translation interpretations, the answer is:

h = -1 and k = -6