Question

Options for the first box: x, y, w, z Options for the second box: Horizontal compressionVertical compressionReflection of the X axisHorizontal shift

Answer 1

`\begin{gathered} \text{Looking at the graph }f(x)=((1)/(2))^x,\text{ we know that} \\ f(-2)=4\rightarrow(-2,4) \\ f(0)=1\rightarrow(0,1) \\ \text{When applied a horizontal shift (x-axis), 3 units to the right. We have the following:} \\ (-2+3,4)\rightarrow(1,4) \\ (0+3,1)\rightarrow(3,1) \\ \text{These two points, }(1,4)\text{ and }(3,1)\text{ is present with graph X. Therefore,} \\ \text{the graph of function }g\text{ is graph X because the graph of the function }g\text{ is the result of a} \\ \text{horizontal shift applied to the graph of function }f. \end{gathered}`