\#2: Graph \( y=2+2^{x-2} \) using \( x=0,1,2,3,4 \) (Count by 1 's up to 8 along the \( y \)-axis) (5 Points)

To graph the function \( y=2+2^{x-2} \) at the specified values of \( x \), we calculate \( y \) for each value: - For \( x=0 \): \( y=2+2^{0-2}=2+2^{-2}=2+\frac{1}{4}=2.25 \) - For \( x=1 \): \( y=2+2^{1-2}=2+2^{-1}=2+\frac{1}{2}=2.5 \) - For \( x=2 \): \( y=2+2^{2-2}=2+2^{0}=2+1=3 \) - For \( x=3 \): \( y=2+2^{3-2}=2+2^{1}=2+2=4 \) - For \( x=4 \): \( y=2+2^{4-2}=2+2^{2}=2+4=6 \) Plotting these points gives us: - \( (0, 2.25) \) - \( (1, 2.5) \) - \( (2, 3) \) - \( (3, 4) \) - \( (4, 6) \) Points can be graphically represented on a coordinate plane, showing growth as \( x \) increases. As \( x \) moves towards higher values, \( y \) increases rapidly due to the exponential component.