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This problem trains for: SAT-I.
h(x)+5 has at least how many x-intercepts?
Adding 5 units to the y-value translates the function up by 5.
After the translation, from the visible part of the graph, only 2 x-intercepts are guaranteed to exist. Note that more intercepts may exist outside of the visible portion of the graph and that, if the entire domain is not visible, and the algebraic expression of the function is not known, there is no indication as to the exact number of intercepts.