Given: Graph of a function is given.
Required: To identify which equation would have real zero(s) corresponding to the x-intercept(s) of the graph.
Explanation: A function's zero(s) are represented on the graph as the x-intercept. Hence we need to solve the given equations for zero(s).
We put the equation equal to zero to solve for zero(s).
The first equation given is
[tex]y=-2^x+4[/tex]
Putting the equation, y=0 gives
[tex]\begin{gathered} -2^x+4=0 \\ -2^x=-4 \\ 2^x=2^2 \\ \Rightarrow x=2 \end{gathered}[/tex]
The second equation given has no x-intercept.
The third equation has an x-intercept at
[tex](-\frac{3}{2},0)[/tex]
The last equation has an x-intercept at
[tex](1,0)[/tex]
Final Answer: Option A is correct.
