The graph shows the function f(x) which equation represents f(x)?

Some times it's really very easy to answer the problem just by looking over the given problem.

For the given graph, we need to observe some(or any) point on the graph that can conclude anything to answer the given problem.

Generally we observe x or y-intercepts of the graph first.

Let us observe the y-intercept of the given graph, because we can see a clear picture of y-intercept there.

By looking on the graph, we can see y-intercept is at -1.

Note: y-intercept is a point on y-axis where value of x is 0.

Now let us observe the given functions in the given options.

First option: If we plug x=0 in the given function, we get f(0)=0.

So, y-intercept for first option is 0.

Second option: If we plug x=0, we get a negative -1 inside radical. Cube root of -1 is -1. On multiplying by -1 we get +1.

So, y-intercept for second option is 1.

Third option : If we plug x=0 in that function, we get 0-1 = -1.

So, the y-intercept for third function is -1.

Therefore, function in third option is the correct function for given graph.

Therefore, third option     is correct option.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is