Question

Which diagram shows the graph of y=-|x-3|?

Can anyone tell me how to solve this step by step?

Answer 1

Graph 4)

Explanation:

Absolute Value

The absolute value of x, written as |x| is a positive number that represents the distance from the origin and the number.

In practice, the absolute value is found writing the number without the negative sign, if present.

For example:

|-3| = 3

|12| = 12

|0| = 0

We are given the function:

y = - | x - 3 |

Since the absolute value is positive, the minus sign before the bars make this function always negative. All options except 4) are automatically discarded because they have positive values for y.

Give x some values: x={-1,0,3,4}

And evaluate y:

x=-1

y = - | -1 - 3 | = - | -4 | = -4

x=0

y = - | 0 - 3 | = - | - 3 | = -3

x=2

y = - | 2 - 3 | - | -1 | = -1

x=3

y = - | 3 - 3 | - | 0 | = 0

x=4

y = - | 4 - 3 | - | 1 | = -1

Plotting these points and drawing the graph, we get the graph shown in option 4)