230k views
5 votes
Describe the graph of y=(2/x+5)-3 to the graph of y= 1/x


please help me :))

Describe the graph of y=(2/x+5)-3 to the graph of y= 1/x please help me :))-example-1
User MetaZebre
by
8.5k points

1 Answer

4 votes

Answer:

The graph of y = (2/(x+5)) - 3 is a transformation of the graph of y = 1/x, which has a vertical asymptote at x = 0 and passes through the point (1,1), by a horizontal shift of 5 units to the left, a vertical stretch of 2 units, and a downward shift of 3 units.

Explanation:

The graph of y = (2/(x+5)) - 3 can be obtained by applying vertical and horizontal transformations to the graph of y = 1/x.

Specifically, we can describe the graph of y = 1/x as the parent function. It has a vertical asymptote at x = 0, a horizontal asymptote at y = 0, and it passes through the point (1,1).

The graph of y = (2/(x+5)) - 3 can be obtained by first shifting the graph of y = 1/x horizontally to the left by 5 units, then vertically stretching it by a factor of 2, and finally shifting it downward by 3 units.

This means that the vertical asymptote of y = 1/x at x = 0 is shifted to x = -5 for y = (2/(x+5)) - 3. The horizontal asymptote of y = 1/x at y = 0 remains the same for y = (2/(x+5)) - 3.

The point (1,1) on the graph of y = 1/x is shifted to (-4,-1) on the graph of y = (2/(x+5)) - 3.

Therefore, the graph of y = (2/(x+5)) - 3 is a transformation of the graph of y = 1/x, which has a vertical asymptote at x = 0 and passes through the point (1,1), by a horizontal shift of 5 units to the left, a vertical stretch of 2 units, and a downward shift of 3 units.

Visually, the graph of y = (2/(x+5)) - 3 will look like a reflected and vertically stretched version of the graph of y = 1/x, with a vertical asymptote at x = -5 and passing through the point (-4,-1).

User Tiago Fabre
by
8.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories