QuestionJuly 15, 2025

Which are points on the graph of y=1.5+lceil xrceil Select three options (-4.5,-2.5) (-0.8,0.5) (7.9,9.5) (4.5,6) (1.3,3.5)

Which are points on the graph of y=1.5+lceil xrceil Select three options (-4.5,-2.5) (-0.8,0.5) (7.9,9.5) (4.5,6) (1.3,3.5)
Which are points on the graph of y=1.5+lceil xrceil Select three options (-4.5,-2.5) (-0.8,0.5) (7.9,9.5) (4.5,6) (1.3,3.5)

Solution
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Answer

(-4.5,-2.5), (7.9,9.5), (1.3,3.5) Explanation 1. Calculate \lceil x \rceil For each point, calculate \lceil x \rceil. - (-4.5,-2.5): \lceil -4.5 \rceil = -4 - (-0.8,0.5): \lceil -0.8 \rceil = 0 - (7.9,9.5): \lceil 7.9 \rceil = 8 - (4.5,6): \lceil 4.5 \rceil = 5 - (1.3,3.5): \lceil 1.3 \rceil = 2 2. Apply the formula y = 1.5 + \lceil x \rceil Substitute \lceil x \rceil into the equation to find y. - (-4.5,-2.5): y = 1.5 + (-4) = -2.5 - (-0.8,0.5): y = 1.5 + 0 = 1.5 - (7.9,9.5): y = 1.5 + 8 = 9.5 - (4.5,6): y = 1.5 + 5 = 6.5 - (1.3,3.5): y = 1.5 + 2 = 3.5 3. Verify matching points Check if calculated y matches given y for each point. - (-4.5,-2.5): Matches - (-0.8,0.5): Does not match - (7.9,9.5): Matches - (4.5,6): Does not match - (1.3,3.5): Matches

Explanation

1. Calculate $\lceil x \rceil$<br /> For each point, calculate $\lceil x \rceil$.<br />- $(-4.5,-2.5)$: $\lceil -4.5 \rceil = -4$<br />- $(-0.8,0.5)$: $\lceil -0.8 \rceil = 0$<br />- $(7.9,9.5)$: $\lceil 7.9 \rceil = 8$<br />- $(4.5,6)$: $\lceil 4.5 \rceil = 5$<br />- $(1.3,3.5)$: $\lceil 1.3 \rceil = 2$<br /><br />2. Apply the formula $y = 1.5 + \lceil x \rceil$<br /> Substitute $\lceil x \rceil$ into the equation to find $y$.<br />- $(-4.5,-2.5)$: $y = 1.5 + (-4) = -2.5$<br />- $(-0.8,0.5)$: $y = 1.5 + 0 = 1.5$<br />- $(7.9,9.5)$: $y = 1.5 + 8 = 9.5$<br />- $(4.5,6)$: $y = 1.5 + 5 = 6.5$<br />- $(1.3,3.5)$: $y = 1.5 + 2 = 3.5$<br /><br />3. Verify matching points<br /> Check if calculated $y$ matches given $y$ for each point.<br />- $(-4.5,-2.5)$: Matches<br />- $(-0.8,0.5)$: Does not match<br />- $(7.9,9.5)$: Matches<br />- $(4.5,6)$: Does not match<br />- $(1.3,3.5)$: Matches
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