Home > Algebra > Graphs of Absolute Value Equations

How do you find the critical numbers of an absolute value equation f(x) = |x + 3| - 1?

Answer 1

There is one critical point: #x = -3, y = -1#

Critical points are minima, maxima, and points where #f'(x) = 0#.

Since this is a v-shaped absolute value function, there is no point where f'(x) = 0. However, there is one extremum. It is a minimum located at #x = -3#, and it is the point #(-3, -1)#.

You can figure this out by looking at how #f(x) = |x+3|-1# is a modification of its parent function #f(x) = |x|#. It is shifted left 3 and down 1, so the local minimum from the parent function is also shifted left 3 and down 1.

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

Answer 2

Kennedy Adams

To find the critical numbers of the absolute value equation ( f(x) = |x + 3| - 1 ), set the expression inside the absolute value bars equal to zero and solve for ( x ):

[ x + 3 = 0 ] [ x = -3 ]

The critical number is ( x = -3 ).

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.