Question

unit test
unit test complete
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01:32
the graph of ( h(x) = |x - 10| + 6 ) is shown. on which interval is this graph increasing?
( \bigcirc (-infty, 6) )
( \bigcirc (-infty, 10) )
( \bigcirc (6, infty) )
( \bigcirc (10, infty) )
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Explanation:

Step1: Identify vertex of absolute value function

The function is \( h(x) = |x - 10| + 6 \), which has the form \( |x - a| + b \). The vertex is at \( (a, b) = (10, 6) \).

Step2: Determine increasing interval

Absolute value functions open upward (since coefficient of absolute value is positive). They decrease left of the vertex and increase right of the vertex. So the graph increases for \( x > 10 \), i.e., interval \( (10, ∞) \).

Answer:

D. (10, ∞)