Your friend hands you a graph of the performance statistics of the latest powerboat to be produced. He says, “I know this graph is f(x) = –2(x – 4)3 – 3 but I can’t remember how it is related to the graph of x3.” Explain to your friend how the graph f(x) is a translation of the graph x3.
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where does the x3 even come from?
They took the graph of \(x^3\), and used some combination of rotation, translation, and stretching to get f(x).
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What's a, h, and k?|dw:1441294455335:dw|
would u like me to factor that?
no. just match up the numbers from your function written on the bottom, to you the format written on top.
Each of those letters represent something a transformation to the function. For example \(a = -2\). What are h and k?
\(a\) represents a vertical stretch. Since \(a\) is negative, the function has been reflected over the x-axis.
\(h\) represents a horizontal shift. Positive is right, negative is left.
\(k\) is vertical shift, positive is up, negative is down.