The best way to answer this question would be to try out the choices that are available. Use the choices to find the value of y for each value of x.
Let's try the first one.
[tex]y=5(2^x)+4[/tex][tex]y=5(2^x)+4[/tex]Let's solve for y when x = -2.
[tex]\begin{gathered} y=5(2^{-2})+4 \\ y=5(\frac{1}{2^2})+4 \\ y=5(0.25)+4 \\ y=5.25 \end{gathered}[/tex]Because y = 5.25 and not 2.25 when we use the first equation, then that option is wrong. Let's try the second one.
[tex]y=-5(2^x)-4[/tex]Again, when x = -2,
[tex]\begin{gathered} y=-5(2^{-2})-4 \\ y=-5(\frac{1}{2^2})-4 \\ y=-5(0.25)-4 \\ y=-1.25-4 \\ y=-5.25 \end{gathered}[/tex]The answer is -5.25, which means this option is also wrong. Let's try the third one.
[tex]y=-5(2^x)+4[/tex][tex]\begin{gathered} y=-5(2^{-2})+4 \\ y=-5(\frac{1}{2^2})+4 \\ y=-5(0.25)+4 \\ y=-1.25+4 \\ y=2.75 \end{gathered}[/tex]Because the y-value is 2.75, we can try out the other values of x to make sure that it is also correct when the values of x are changed.
For x = -1:
[tex]\begin{gathered} y=-5(2^{-1})+4 \\ y=-5(\frac{1}{2})+4 \\ y=-5(0.5)+4 \\ y=-2.5+4 \\ y=1.5 \end{gathered}[/tex]For x = 0:
[tex]\begin{gathered} y=-5(2^0)+4 \\ y=-5(1)+4 \\ y=-5+4 \\ y=-1 \end{gathered}[/tex]Foor x = 1:
[tex]\begin{gathered} y=-5(2^1)+4 \\ y=-5(2)+4 \\ y=-10+4 \\ y=-6 \end{gathered}[/tex]We see that for almost all of the values of x, the y-values are the same as those given in the table. Since we have tried 4 points already, it is safe to assume that the third option is the correct answer.
The answer is y = -5(2^x)+4.
