What is the equation of the function shown in the graph, given the equation of the parent function is f(x)=1.5x ?

g(x)=1.5x−2

g(x)=1.5x−3

g(x)=1.5x−4

g(x)=1.5x+2
an exponential function on a coordinate plane with x and y axis in increments of 1 increasing from negative 5 to 5. the function increases from left to right beginning infinitely close in the third quadrant to a dashed horizontal line at y equals negative 4. the function increases through begin ordered pair 0 comma negative 3 end ordered pair and continues to increase through begin ordered pair 2 comma negative 1.75 end ordered pair. the function continues to increase through the second quadrant and out of the first quadrant.

Step-by-step explanation:

Given:

The parent function is given as:

Let us consider a point on and compare their transformation.

The easiest point to consider is the y-intercept. At the y-intercept, the value of 'x' is 0.

The y-intercept of the function is for . So,

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

Now, as per question, the transformed function passes through the point (0, -3). Therefore,

The function in the graph has the y-intercept equal to -3  as at y-intercept, the 'x' value is 0.

Therefore, the y-intercept of is the point (0,-3).

Now, consider the transformation for the points (0, 1) and (0, -3).

Here, the 'x' value remains the same but the 'y' values decreases by 4 units. So, the rule will be:

As per translation rules, if C units is added to 'y' value, then the graph moves up if 'C' is positive and moves down if 'C' is negative.

Also, the equation is of the form:

Here, .

Therefore, the graph shifts down by 4 units.

The equation of the function is given as:

step-by-step explanation: