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Please help me figure out the problem step by step

Please help me figure out the problem step by step-example-1

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To find the graph of the first and the second function, let's substitute x by 1 and find the function that has the corresponding y value.

a)


\begin{gathered} f(x)=2^x \\ f(1)=2^1 \\ f(1)=2 \end{gathered}

The graph that has the point (1, 2) is the green graph.

b)


\begin{gathered} f(x)=3^x \\ f(1)=3^1 \\ f(1)=3 \end{gathered}

The graph that has the point (1, 3) is the yellow graph.

To find the graph of the third and the fourth function, let's substitute x by -1 and find the function that has the corresponding y value.

c)


\begin{gathered} f(x)=((1)/(2))^x \\ f(-1)=((1)/(2))^(-1) \\ f(-1)=((2)/(1))^1 \\ f(-1)=2 \end{gathered}

The graph that has the point (-1, 2) is the blue graph.

d)


\begin{gathered} f(x)=((1)/(3))^x \\ f(-1)=((1)/(3))^(-1) \\ f(-1)=((3)/(1))^1 \\ f(-1)=3 \end{gathered}

The graph that has the point (-1, 3) is the red graph.

Answer:


\begin{gathered} f(x)=2^x\Rightarrow g \\ f(x)=3^x\operatorname{\Rightarrow}y \\ f(x)=((1)/(2))^x\operatorname{\Rightarrow}b \\ f(x)=((1)/(3))^x\operatorname{\Rightarrow}r \end{gathered}

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