Question

What is g(x)? (apex algebra 1 semester 2 2019).

Answer 1

D.
`g(x)=-2^x`

Explanation:

We can use a process of elimination in order to easily solve this.

The shape of
`g(x)=-|x|` will be two diagonal lines that meet at (0,0)

`g(x)=-x^2` Will be an upside down parabola

`g(x)=-x` Will be a line with a slope of -1.

This means that the answer must be D

Answer 2

The correct option is D.

Explanation:

From the given graph it is clear that the y-intercept of the function is -1. It means the graph passes through (0,-1).

Check each function, whether the function passes through the point (0,-1) or not. Substitute x=0 it each function to find the y-intercept.

In option A,

`g(x)=|x|`

`g(0)=|0|=0`

The y-intercept of the function is at (0,0).

In option B,

`g(x)=x^2`

`g(0)=0^2=0`

The y-intercept of the function is at (0,0).

In option C,

`g(x)=x`

`g(0)=0`

The y-intercept of the function is at (0,0).

In option D,

`g(x)=-2^x`

`g(0)=-1`

The y-intercept of the function is at (0,-1).

The graph of
`g(x)=-2^x` passes through the point (0,-1).

Therefore the correct option is D.