A translation of (x -3, y + 4) means

Answer:

you subtract a constant from your x in the original function you shift the graph in the positive direction by that number of units.

And if you subtract a constant from your y in the original function you move its graph down by that number of units.

Your original function was y=4x. When you solve for the root of the denominator, you find the vertical asymptote. In this case, it is x=0, i.e. the y-axis.

And when x goes to ∞, y=4∞=0 which means your horizontal asymptote is y=0, i.e. the x-axis. Here is the graph:



Now, you can see the transformation of y=4x below. As is evident, it has shifted 4 units to the right and 3 units down with vertical asymptote at x=4 and horizontal asymptote at y=−3.



Answer link



Harold Walden

Jan 15, 2018

translation of 4 units right

translation of 3 units down

y=4x−4−3

Explanation:

translation of 4 units right

translation of 3 units down

y=f(x)→y=f(x−4)−3

y=4x−4−3

Step-by-step explanation:

you subtract a constant from your x in the original function you shift the graph in the positive direction by that number of units.

And if you subtract a constant from your y in the original function you move its graph down by that number of units.

Your original function was y=4x. When you solve for the root of the denominator, you find the vertical asymptote. In this case, it is x=0, i.e. the y-axis.

And when x goes to ∞, y=4∞=0 which means your horizontal asymptote is y=0, i.e. the x-axis. Here is the graph:



Now, you can see the transformation of y=4x below. As is evident, it has shifted 4 units to the right and 3 units down with vertical asymptote at x=4 and horizontal asymptote at y=−3.



Answer link



Harold Walden

Jan 15, 2018

translation of 4 units right

translation of 3 units down

y=4x−4−3

Explanation:

translation of 4 units right

translation of 3 units down

y=f(x)→y=f(x−4)−3

y=4x−4−3

translation of 4 units right

translation of 3 units down

y=4x−4−3

Explanation:

translation of 4 units right

translation of 3 units down

y=f(x)→y=f(x−4)−3

y=4x−4−3

I hope it helps :)

Answer link

A translation of (x - 3, y + 4) means that each point in the original graph is moved horizontally by 3 units to the right and vertically by 4 units upward to create a new graph.

For any point (x, y) on the original graph, the corresponding point (x', y') on the translated graph is obtained by adding:

x' = x - 3

y' = y + 4

This type of translation is also known as a "horizontal translation to the right by 3 units" and a "vertical translation upward by 4 units." The "x - 3" part represents the horizontal movement, and the "y + 4" part represents the vertical movement.

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