Answer to Question #225749 in Algebra for harj

Question

Find a formula for an exponential or logarithmic function that matches each of the four graphs below. Write your formula carefully (on paper), taking care to use proper mathematical notation. Then scan or take a picture of your answers, and upload them for grading by your teacher. Provide complete explanations of how you arrived at your answers.

Answer 1

The graphs are taken from this task posted on site https://www.chegg.com/homework-help/questions-and-answers/find-formula-exponential-logarithmic-function-matches-four-graphs--write-formula-carefully-q50145926 because they are not attached in the task here.

1) This graphs seems to be hyperbola due to its shape, but it intercepts the axis OX, so there is a horizontal parallel transfer made on this graph. the formula of hyperbola is y=k/x, k is constant. Looking at the picture, we can see that whatever the horizontal transfer is, we would have points y=10 and y=2, only x would change, and at this two points A1(10, x1) and A2(2, x2) x2 is bigger than x1 by 1. So we can make the equation system:

$$k/x_1=10$$

$$k/x_2=2$$

$$x_1+1=x_2$$

$$k=10x_1=2x_2$$

$$10x_1=2(x_1+1)=2x_1+2$$

$$8x_1=2$$

$$x_1=2/8=1/4=0.25;y_1=10$$ $$y=k/x=>k=y*x=10*0.25=2.25$$

So we have the original formula, before the transfer

$$y=2.25/x$$

If the x=1, we would have y=2.25, but we have y=2. We should find x that makes y=2. x=k/y=2.25/2=1.125, and on the graph we have x=1 when y=2. So the graph was moved on 0.125 points left, its formula is y=(2.25/x)-0.125