Question

Which equation represents the function graphed on the coordinate plane?????

Answer 1

Answer:

All equations represent the function graphed on the coordinates plane.

Step-by-step explanation:

Given :functions.

To find : Which equation represent the function graphed.

Solution : We have given that:

The parent modulus function is:

g(x) = |x|

It is centered at the origin and opens upwards.A coefficient inside the modulus |x+k| means that the function is shifted along the x-axis.

A coefficient outside the modulus |x| + h means that the function is shifted along the y-axis

Now, let's check each of the options:

g(x) = |x+4| - 2 :

This function is shifted 4 units to the left and 2 units down. It will be centered at (-4,-2). Check the blue graph in the attachment.

g(x) = |x-4| - 2 :

This function is shifted 4 units to the right and 2 units down. It will be centered at (4,-2). Check the black graph in the attachment.

g(x) = |x-2| - 4 :

This function is shifted 2 units to the right and 4 units down. It will be centered at (2,-4). Check the red graph in the attachment.

g(x) = |x-2| + 4 :

This function is shifted 2 units to the right and 4 units up. It will be centered at (2,4).

Therefore, All equations represent the function graphed on the coordinates plane.

Answer 2

Since you haven't provided the graph, I'll explain each one and you choose the one suiting your given.

The parent modulus function is:

g(x) = |x|

It is centered at the origin and opens upwards.

A coefficient inside the modulus |x+k| means that the function is shifted along the x-axis

If "k" is positive, the shift will be to the left. If "k" is negative, the shift will be to the right.

A coefficient outside the modulus |x| + h means that the function is shifted along the y-axis

If "h" is positive, the shift will be upwards. If "h" is negative, the shift will be downwards.

Now, let's check each of the options:

g(x) = |x+4| - 2 :

This function is shifted 4 units to the left and 2 units down. It will be centered at (-4,-2). Check the blue graph in the attachment.

g(x) = |x-4| - 2 :

This function is shifted 4 units to the right and 2 units down. It will be centered at (4,-2). Check the black graph in the attachment.

g(x) = |x-2| - 4 :

This function is shifted 2 units to the right and 4 units down. It will be centered at (2,-4). Check the red graph in the attachment.

g(x) = |x-2| + 4 :

This function is shifted 2 units to the right and 4 units up. It will be centered at (2,4). Check the green graph in the attachment.

All 4 graphs are shown in the attached picture.

Hope this helps :)