Reasoning About Exponential Graphs

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CCSS.HSF-IF.C.7E

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CCSS.HSF-IF.C.7E

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CCSS.HSF-IF.C.7E

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CCSS.HSF.LE.A.2

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CCSS.8.F.A.2

CCSS.HSF.IF.C.9

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CCSS.HSF.LE.A.2

Here are equations defining three exponential functions \(f\), \(g\), and \(h\). Which of these functions grows the least quickly? Which one grows the most quickly? Explain how you know. The three given graphs represent \(f\), \(g\), and \(h\). Which graph corresponds to each function? Why do all three graphs share the same intersection point with the vertical axis?

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CCSS.HSF-IF.C.7E

Here are graphs of three exponential equations. Match each equation with its graph.

• y = 20 \cdot 3^x

• y = 50 \cdot 3^x

• y = 100 \cdot 3^x

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CCSS.HSF.LE.A.2

If \(B\) is the graph of \(h\) and \(h\) is defined by \(h(x) = a\cdot b^x\), what can you say about \(a\) and \(b\)? Explain your reasoning.

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CCSS.HSF-IF.C.7E

Here is a graph of \(y = 100 \cdot 2^x\). On the same coordinate plane: Sketch a graph of \(y = 50\cdot 2^x\) and label it A. Sketch a graph of \(y = 200 \cdot 2^x\) and label it B.

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CCSS.HSF-IF.C.7E