Which of the following is the function representing the graph below? graph begins in the third quadrant near the line y equals negative 3 and increases slowly while crossing the ordered pair 0, negative 2. when the graph enters the first quadrant, it begins to increase quickly throughout the graph.
f(x) = 4x
f(x) = 4x − 3
f(x) = 4x + 3
f(x) = 4(x + 3)

  f(x) = 4^x -3

Step-by-step explanation:

All of the listed functions are linear functions with a constant slope of 4. None of them goes through the point (0, -2).

__

So, we assume that there is a missing exponentiation operator, and that these are supposed to be exponential functions. If the horizontal asymptote is -3, then there is only one answer choice that makes any sense:

  f(x) = 4^x -3

_____

The minimum value of 4^z for any z will be near zero. In order to make it be near -3, 3 must be subtracted from the exponential term.

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.