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Which of the following represents the graph of this equation? y=|x|-1

if someone could explain how you got the answer i'd really appreciate it. having trouble with the concept.

Which of the following represents the graph of this equation? y=|x|-1 if someone could-example-1
User Aiuspaktyn
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1 Answer

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First, let’s look at the parent function. The parent function is the original function in which changes are made to create a new function.

The parent function is

y=|x|

The changes made to make the function in the question is the function will be translated down 1 unit, hence why -1 trails behind the absolute value bars. So, this simply means all y-values of the function will be translated down 1 unit, and the x-values stay the same since the -1 only affects the y-values.

So, let’s graph y=|x| and simply subtract 1 from every output (y-value):

Remember, we must input an x-value into the function, and the function will manipulate this value to get an output value (y-value).

Let’s create a list of x and y values according to the parent function:

x=0

y=|0|——>y=0

Coordinate: (0, 0)

x=-1

y=|-1|——>y=1

Coordinate: (-1, 1)

x=-2

y=|-2|——>y=2

Coordinate: (-2, 2)

x=1

y=|1|—->1

Coordinate: (1, 1)

x=2

y=|2|——>2

Coordinate: (2, 2)

When we graph the ordered pairs, the function will intercept the origin and appear like a “V.” Now, the modified function has the trailing -1, indicating we must subtract 1 from the y-coordinates. Let’s create a new table of values to see this:

x=-2

y=|-2|-1 ——>y=2-1—>y=1

Coordinate: (-2, 1)

Recall that in the parent function, when x=-2, y=2. Now, when x=-2, y=1, so the y-coordinate is translated down 1 unit.

x=-1

y=|-1|-1 ——> y=1-1 —-> y=0

Coordinate: (-1, 0)

x=0

y=|0|-1 ——>y=-1

Coordinate: (0, -1)

x=1

y=|1|-1 ——> y=1-1 ——> y=0

Coordinate (1, 0)

x=2

y=|2|-1 ——> y=2-1 ——> y=1

Coordinate: (2, 1)

So, if you compare the modified function with the parent function, the x-values Eemian untouched, while the y-values are shifted down 1 unit. This is what the -1 does to the function. The -1 is outside the absolute value box meaning it affects the y-coordinates. The -1 would have to be subtracting the x to affect the x-coordinates.

So, the answer is graph B.)

User Nick Palmer
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