Question

Which graph represents the function f(x)=−2x−1 ?

Answer 1

The third graph represents the function
`f(x)=-2^x-1`

Explanation:

We have the function,
`f(x)=-2^x-1`.

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
`f(0)=-2^0-1` i.e.
`f(0)=-1-1` 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
`x\rightarrow \infty`, then
`f(x)\rightarrow -\infty` and
`x\rightarrow -\infty`, then
`f(x)\rightarrow -1`

Hence, the third graph represents the function
`f(x)=-2^x-1`.

Answer 2

-(2^x) - 1 will have a y-intercept of -1-1 = -2, a horizontal asymptote of y=-1, and will be decreasing everywhere. The third selection is the graph that has these characteristics.