Graph the function rule. Explain why the graph is continuous or discrete. Graph y=−|x|+2y=−∣x∣+2

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Ezra Herbert · Accepted Answer

To graph the function rule y=−|t|+2, we choose several input values x and find the corresponding output values y. Then we create a table showing those inputs and outputs. Finally, we plot these pairs of input, output (x,y) on a rectangular coordinate system and join them. We find the output values x of the given function rule at x=−2,−1,0,1 and 2. Substituting x=−2 in the expression −|x|+2, we get y=−|−2|+2 =−2+2 [evaluate the absolute value] =0 [perform the addition} Substituting x=−1 in the expression −|x|+2, we get y=−|−1|+2 =−1+2[evaluate the absolute value] =1 [perform the addition] Substituting x=0 in the expression −|x|+2, we get =−|0|+2 [evaluate the absolute value] =2 [perform the addition] Substituting x=1 in the expression −|x|+2, we get y=−|1|+2 =−1+2 [evaluete the absolute value] =1 [perform the addition] Substituting x=2 in the expression −|x|+2, we get y=−|2|+2 =−2+2 [evaluate the absolute value] =0 [perform the addition] The following table shows the values and the corresponding ordered pairs. x−2−1012y01210 Now plotting the ordered pairs on a rectangular coordinate system, we get the following graph of the function rule y=−|x|+2 [Graph]

Graph the function rule. Explain why the graph is continuous or discrete. Graph y=-|x|+2y=−∣x∣+2

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