How to graph y= - x+3+2?

Question

x+3 are in an absolute value bars

Answer 1

use a graphing calculator

Answer 2

The function is y= -|x+3|+2.

There are two methods:

1) break the function:

|x+3|=x+3 when x+3=>0 or x=> -3

|x+3|= -(x+3) when x+3<0 or x< -3

When x=> -3, y= -(x+3)+2= -x-3+2= -x-1,which is straight line with slope -1 & y-intercept= -1.

When x< -3, y= -[-(x+3)]+2= x+3+2=x+5,which is straight line with slope 1 & y-intercept= 5.

2)Draw graph of y=x+2. Take reflection about X-axis when graph is ABOVE X-axis. this is graph of y= -|x+2|

shift the graph two units upwards therefore graph of y= -|x+3|+2 is drawn.

You can use | (Verticle bar) to show absolute value function.

E-Mail me if any further query is required.

Answer 3

Clear the absolute-value bars by splitting the equation into two cases, one for each sign:

                     y= -x+3+2           and         y= x+3+2

Simplify by combining like terms:

                     y= -x+5               and         y= x+5

Use a chart to find at least two ordered pairs for each equation, such as:

x    (-x+5)    y    (x,y)                

0    (-0+5)    5    (0,5)                              

1    (-1+5)    4    (1,4)                              

and

x    (x+5)    y    (x,y)

0    (0+5)    5    (0,5)

1    (1+5)    6    (1,6)

Plot the points for each equation and connect them: both lines form a V with the wide part facing left. The lines intercept at (0,5).

Hope I helped! :)