QuestionAugust 26, 2025

Which of the following functions has a range of yvert ygeqslant -11 ? (1 point) h(x)=vert x+11vert +7 h(x)=vert x+7vert -11 h(x)=vert x+7vert +11 h(x)=vert x+11vert -7

Which of the following functions has a range of yvert ygeqslant -11 ? (1 point) h(x)=vert x+11vert +7 h(x)=vert x+7vert -11 h(x)=vert x+7vert +11 h(x)=vert x+11vert -7
Which of the following functions has a range of  yvert ygeqslant -11  ? (1 point)
h(x)=vert x+11vert +7
h(x)=vert x+7vert -11
h(x)=vert x+7vert +11
h(x)=vert x+11vert -7

Solution
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Answer

h(x)=\vert x+7\vert -11 Explanation 1. Analyze the function h(x)=\vert x+11\vert +7 The minimum value of \vert x+11\vert is 0, so the minimum value of h(x) is 0 + 7 = 7. The range is \{ y \vert y \geqslant 7 \}. 2. Analyze the function h(x)=\vert x+7\vert -11 The minimum value of \vert x+7\vert is 0, so the minimum value of h(x) is 0 - 11 = -11. The range is \{ y \vert y \geqslant -11 \}. 3. Analyze the function h(x)=\vert x+7\vert +11 The minimum value of \vert x+7\vert is 0, so the minimum value of h(x) is 0 + 11 = 11. The range is \{ y \vert y \geqslant 11 \}. 4. Analyze the function h(x)=\vert x+11\vert -7 The minimum value of \vert x+11\vert is 0, so the minimum value of h(x) is 0 - 7 = -7. The range is \{ y \vert y \geqslant -7 \}.

Explanation

1. Analyze the function $h(x)=\vert x+11\vert +7$<br /> The minimum value of $\vert x+11\vert$ is 0, so the minimum value of $h(x)$ is $0 + 7 = 7$. The range is $\{ y \vert y \geqslant 7 \}$.<br />2. Analyze the function $h(x)=\vert x+7\vert -11$<br /> The minimum value of $\vert x+7\vert$ is 0, so the minimum value of $h(x)$ is $0 - 11 = -11$. The range is $\{ y \vert y \geqslant -11 \}$.<br />3. Analyze the function $h(x)=\vert x+7\vert +11$<br /> The minimum value of $\vert x+7\vert$ is 0, so the minimum value of $h(x)$ is $0 + 11 = 11$. The range is $\{ y \vert y \geqslant 11 \}$.<br />4. Analyze the function $h(x)=\vert x+11\vert -7$<br /> The minimum value of $\vert x+11\vert$ is 0, so the minimum value of $h(x)$ is $0 - 7 = -7$. The range is $\{ y \vert y \geqslant -7 \}$.
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