Home > Algebra > Graphs in the Coordinate Plane

How do you graph #y = | x + 3| -2#?

Answer 1

Ethan Adkins

graph{|x+3|-2 [-10, 10, -5, 5]}

#y#-intercept:

#x = 0#

#|x+3| = 0+3# #= 3#

#|x+3|-2=3-2=1#

#y#-intercept: #1#

#x#-intercept:

#y=0#

#|x+3|-2 = 0#

#|x+3|=2#

#x+3 = 2 or -2#

#x#-intercept: #-1 or -5#

the axis of symmetry on the graph is the vertical line #x = -3#.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer 2

Eva Abramson

To graph the function y = |x + 3| - 2, follow these steps:

Identify the vertex of the absolute value function, which occurs at the point (-3, -2).
Plot the vertex on the coordinate plane.
Choose two additional points to the left and right of the vertex.
Calculate the y-values for each point using the equation y = |x + 3| - 2.
Plot the additional points on the graph.
Connect the points with a smooth curve, reflecting the shape of the absolute value function.
Label the axes and any critical points on the graph for clarity.

By signing up, you agree to our Terms of Service and Privacy Policy

Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.