## hilltaylor13 Group Title How do the graphs of y = 1/x and y =3/x – 4 compare? will receive medal for right answer! one year ago one year ago

1. hilltaylor13 Group Title

answer choices: Compared to the graph of y =1/x , the graph of y =3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units left. Compared to the graph of y =1/x , the graph of y =3/x – 4 is a vertical shrink by a factor of 3 and a translation of 4 units up. Compared to the graph of y =1/x , the graph of y =3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units down. Compared to the graph of y =1/x , the graph of y =3/x – 4 is a vertical shrink by a factor of 3 and a translation of 4 units down.

2. ZeHanz Group Title

$$\dfrac{3}{x}-4=3 \cdot \dfrac{1}{x}-4$$, so there have been two changes from 1/x. The 3 times 1/x means every outcome will be 3 times as big. Can you imagine what the effect on the graph is?

3. ZeHanz Group Title

Once you've got that, imagine what subtracting 4 from every y-coordinate does with points on the graph.

4. hilltaylor13 Group Title

yeah, i have no idea.

5. ZeHanz Group Title

Look at the answers. It is about stretching and shrinking on the one hand, and about translation on the other. The numbers and calculations we have are: $$\cdot~ 3$$ and $$-4$$. Now if you again think about what it means when you take the outcomes (=how high points lie on the graph) and multiply them with 3. E.g. suppose point (1, 1) is on the graph of y=1/x (it is). Multiply the y-coordinate with 3. New point: (1,3). Also (2, ½) is on the graph of y=1/x. Multiply the y-coordinate with 3. New point: (2, 1½). What is happening?

6. ZeHanz Group Title

You could also say: every point is getting 3 times farther away from the x-axis. How would you call that? (again, look at the answers)

7. hilltaylor13 Group Title

a?

8. hilltaylor13 Group Title

i'm guessing a or c because of the vertical stretch

9. hashim12atd Group Title

It should go down by four units and and stretched 3 times. you should try to think what happens you multiply only one coordinate with a number. . Try to experiment on a graphing software, there you will grasp the idea how graphs are changed when coffeceints of variable s are changed.