Answer:
[tex]f(x)=3^x+4[/tex]
Step-by-step explanation:
In the graph curve passes through the point [tex](0,5)[/tex] and [tex]f(x)\rightarrow4[/tex] when [tex]x\rightarrow-\infty.[/tex]
Check these two conditions for each function.
[tex]f(x)=3^x+4\\\ \lim_{x \to -\infty} f(x) =\lim_{x\rightarrow-\infty}3^x+4=4[/tex]
When [tex]f(x)=3x+5[/tex] or [tex]4x+4[/tex] or [tex]4x+5[/tex]
[tex]\lim_{x \to -\infty} f(x)=-\infty[/tex]
Hence only [tex]f(x)=3^x+4[/tex] satisfies the condition [tex]\lim_{x \to -\infty} f(x)=4[/tex]
Check if [tex](0,5)[/tex] is the point of [tex]f(x)=3^x+4[/tex]
[tex]f(0)=3^0+4=1+4=5[/tex]
Hence [tex]f(x)=3^x+4[/tex] represents the given graph.
