The student’s graph is not a correct representation of the function. The linear part should end at the open circle at (-2, 1), but it appears to have been incorrectly drawn, and the quadratic section should include the closed endpoint at (-2, 3) and correctly reflect the vertex at (0, -1) and the closed endpoint at (1, 0).
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Feature
The graph of a piecewise function is shown.The graph of a linear function starts in quadrant 3, has a positive slope, and a right endpoint at open circle left-parenthesis negative 2 comma 1 right parenthesis. It also shows a portion of a quadratic function opening upwards with left endpoint closed circle left-parenthesis negative 2 comma 3 right-parenthesis, vertex left-parenthesis 0 comma negative 1 right-parenthesis, and right endpoint closed circle left-parenthesis 1 comma 0 right-parenthesis. It also shows the graph of a logarithmic function with left endpoint open circle left-parenthesis 1 comma 2 right-parenthesis. The logarithmic function increases as it goes to the right and passes through the point left-parenthesis 5 comma 3 right parenthesis.
Question
Use the graph to answer the question.
A student was given the piecewise functionf left parenthesis x right parenthesis equals enlarged left brace start layout 1st row x plus 3 comma x less than or equal negative 2 2nd row x squared minus 1 comma negative 2 less than x less than 1 3rd row log subscript 2 baseline left parenthesis negative x plus 3 right parenthesis comma 1 less than or equals x less than 3 end layout and created this graph of the function.
Is the student’s graph a correct representation of the function? If not, explain how it should be corrected in 2 short complete sentences
1 answer
1 answer