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)

Question

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

Answer 1

To translate a hexagon (or any shape) 7 units to the left on the coordinate grid, you need to subtract 7 from the x-coordinate of each point of the shape.

The correct function that represents this translation can be written as:

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

So, the choice that Ella should write is:

f(x) = x - 7

Answer 2

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

(4,−3)
left parenthesis 4 comma negative 3 right parenthesis

(−2,8)
left parenthesis negative 2 comma 8 right parenthesis

(0,1)
left parenthesis 0 comma 1 right parenthesis

(1,0)

Answer 3

To find the new coordinates of the lowest vertex of the triangle after the translation, we start by identifying the lowest vertex from the original coordinates.

The vertices of the triangle are:

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

Among these, the lowest vertex is \((-1, -5)\).

Now, we need to translate this vertex 5 units up and 2 units to the right:

1. To translate 5 units up, we add 5 to the y-coordinate: \[ -5 + 5 = 0 \]

2. To translate 2 units to the right, we add 2 to the x-coordinate: \[ -1 + 2 = 1 \]

Thus, the new coordinates of the lowest vertex after the translation will be \((1, 0)\).

Therefore, the correct response is:

(1, 0)

Answer 4

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+1
g left parenthesis y right parenthesis equals y plus 1

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

Answer 5

The translation of the point \((2, -5)\) to \((2, -6)\) indicates a vertical movement. Specifically, the y-coordinate changes from \(-5\) to \(-6\), which is a downward movement of 1 unit.

In order to represent this translation as a function, we note that to get the new y-coordinate from the original, we need to subtract 1 from the original y-coordinate:

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

Therefore, the function that shows the appropriate translation is:

g(y) = y - 1