Graph the following function on the axes provided. f(x) = -5.2 – 21 2 – 9 for x < -3=”” for=”” x=””> 4 Click and drag to make a line. Click the line to delete it. Click on an endpoint of a line to change it. y 10 9 8 7 6 5 4 3 1 2 8 -6 -5 – 1 w 5 6 7 9 10 -1 -5 -6 -7 -10<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n To graph the function correctly and explain it, we first need to clarify the piecewise function<\/strong>, which seems garbled in your question. Based on your input, it appears to be a piecewise function defined as: f(x)={\u22125.2,for x<\u22123\u221221×2\u22129,for x>4f(x) = \\begin{cases} -5.2, & \\text{for } x < -3 \\\\ -21x^2 – 9, & \\text{for } x > 4 \\end{cases}<\/p>\n\n\n\n Let\u2019s break this down:<\/p>\n\n\n\n This part is a horizontal line<\/strong> at y=\u22125.2y = -5.2, and it only exists for values where x<\u22123x < -3. So you would draw a straight line horizontally at y=\u22125.2y = -5.2, extending leftward<\/strong> from x=\u22123x = -3. The point at x=\u22123x = -3 is not included<\/strong>, so place an open circle<\/strong> at (\u22123,\u22125.2)(-3, -5.2).<\/p>\n\n\n\n This part is a quadratic equation<\/strong> (a parabola). Since the coefficient of x2x^2 is negative, the parabola opens downward<\/strong>. But we only graph the part for x>4x > 4.<\/p>\n\n\n\n Let’s calculate some points for x>4x > 4:<\/p>\n\n\n\n You\u2019ll notice the values quickly drop to large negative numbers. So the graph steeply curves downward to the right of x=4x = 4. Start the parabola right after x=4x = 4<\/strong> with an open circle<\/strong> at x=4x = 4, then plot a curved line downward (left to right).<\/p>\n\n\n\n This is a piecewise-defined function<\/strong>, meaning it behaves differently based on the value of xx. Understanding how to graph this involves analyzing each “piece” separately and applying correct graphing principles.<\/p>\n\n\n\n The first piece of the function is a constant function f(x)=\u22125.2f(x) = -5.2 defined for all values where x<\u22123x < -3. This tells us that no matter what value of xx we choose (as long as it’s less than -3), the value of the function f(x)f(x) is always -5.2. When graphing this, we draw a horizontal line at y=\u22125.2y = -5.2 extending to the left. Since the function only holds for x<\u22123x < -3, and not at x=\u22123x = -3, we indicate this with an open circle<\/strong> at the point (\u22123,\u22125.2)(-3, -5.2), showing that this endpoint is not included.<\/p>\n\n\n\n The second piece of the function is a quadratic expression f(x)=\u221221×2\u22129f(x) = -21x^2 – 9, defined for values where x>4x > 4. This function represents a parabola<\/strong> opening downward due to the negative coefficient of x2x^2. However, the domain restriction of x>4x > 4 means we only draw the part of the parabola to the right of x=4x = 4<\/strong>. We again use an open circle at x=4x = 4 to show this point is not included in the graph. The values of f(x)f(x) in this region drop very rapidly, and the graph curves downward steeply as xx increases.<\/p>\n\n\n\n To summarize, this function is a combination of a flat line (left side) and a steep, downward-opening curve (right side), with a break in the graph between x=\u22123x = -3 and x=4x = 4, where no function is defined. Understanding such behavior is essential in graphing piecewise functions accurately.<\/p>\n","protected":false},"excerpt":{"rendered":" Graph the following function on the axes provided. f(x) = -5.2 – 21 2 – 9 for x < -3=”” for=”” x=””> 4 Click and drag to make a line. Click the line to delete it. 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\n\n\n\n1. Graphing f(x)=\u22125.2f(x) = -5.2 for x<\u22123x < -3:<\/strong><\/h3>\n\n\n\n
\n\n\n\n2. Graphing f(x)=\u221221×2\u22129f(x) = -21x^2 – 9 for x>4x > 4:<\/strong><\/h3>\n\n\n\n
\n
f(5)=\u221221(25)\u22129=\u2212525\u22129=\u2212534f(5) = -21(25) – 9 = -525 – 9 = -534<\/li>\n\n\n\n
f(4.1)=\u221221(16.81)\u22129\u2248\u2212353.01\u22129\u2248\u2212362.01f(4.1) = -21(16.81) – 9 \u2248 -353.01 – 9 \u2248 -362.01<\/li>\n<\/ul>\n\n\n\n
\n\n\n\nImportant Notes for Graphing:<\/strong><\/h3>\n\n\n\n
\n
\n\n\n\nExplanation Summary (300+ Words):<\/strong><\/h3>\n\n\n\n