Answer:
The third graph represents the function [tex]f(x)=-2^x-1[/tex]
Step-by-step explanation:
We have the function, [tex]f(x)=-2^x-1[/tex].
As we know, 'The y-intercept of a function is the point where the graph of the function crosses y-axis'.
i.e. At x=0, we get the y-intercept is [tex]f(0)=-2^0-1[/tex] i.e. [tex]f(0)=-1-1[/tex] i.e. f(0) = -2.
So, the y-intercept of the function is at (0,-2).
Since, out of the four graphs given, we see that, the third graph crosses y-axis at (0,-2).
Moreover, as [tex]x\rightarrow \infty[/tex], then [tex]f(x)\rightarrow -\infty[/tex] and [tex]x\rightarrow -\infty[/tex], then [tex]f(x)\rightarrow -1[/tex]
Hence, the third graph represents the function [tex]f(x)=-2^x-1[/tex].
