QuestionCreate a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

Studdy Solution

STEP 1

Assumptions1. The function is $g(x)=\frac{}{x}$ . We need to create a table and a graph for this function3. We need to describe the graph completely

STEP 2

Let's start by creating a table of values for the function $g(x)=\frac{2}{x}$ . We can choose a few values for $x$ and calculate the corresponding $g(x)$ values.

STEP 3

Choose the values for $x$ . Let's choose -3, -2, -1,0,1,2,3.

STEP 4

Calculate the corresponding $g(x)$ values.
For $x=-3$ , $g(x)=\frac{2}{-3} = -\frac{2}{3}$
For $x=-2$ , $g(x)=\frac{2}{-2} = -1$
For $x=-1$ , $g(x)=\frac{2}{-1} = -2$
For $x=0$ , $g(x)$ is undefined because we cannot divide by zero.
For $x=1$ , $g(x)=\frac{2}{1} =2$
For $x=2$ , $g(x)=\frac{2}{2} =1$
For $x=3$ , $g(x)=\frac{2}{3}$

STEP 5

Now that we have the table of values, we can plot these points on a graph.

STEP 6

Plot the points (-3, -2/3), (-2, -1), (-1, -2), (1,2), (2,1), (3,2/3) on the graph.

STEP 7

Connect the points with a smooth curve to represent the function $g(x)=\frac{2}{x}$ .

STEP 8

The graph of the function $g(x)=\frac{2}{x}$ is a hyperbola. It has two branches, one in the first quadrant and one in the third quadrant. The graph approaches but never reaches the x-axis and y-axis, which are the asymptotes of the graph.

STEP 9

The graph is undefined at $x=$ because we cannot divide by zero. This is why there is a gap in the graph at $x=$ .

STEP 10

The graph is symmetric with respect to the origin. This means that if you rotate the graph180 degrees around the origin, you will get the same graph.

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QuestionCreate a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

Studdy Solution

STEP 1

Assumptions1. The function is $g(x)=\frac{}{x}$ . We need to create a table and a graph for this function3. We need to describe the graph completely

STEP 2

Let's start by creating a table of values for the function $g(x)=\frac{2}{x}$ . We can choose a few values for $x$ and calculate the corresponding $g(x)$ values.

STEP 3

Choose the values for $x$ . Let's choose -3, -2, -1,0,1,2,3.

STEP 4

STEP 5

Now that we have the table of values, we can plot these points on a graph.

STEP 6

Plot the points (-3, -2/3), (-2, -1), (-1, -2), (1,2), (2,1), (3,2/3) on the graph.

STEP 7

Connect the points with a smooth curve to represent the function $g(x)=\frac{2}{x}$ .

STEP 8

The graph of the function $g(x)=\frac{2}{x}$ is a hyperbola. It has two branches, one in the first quadrant and one in the third quadrant. The graph approaches but never reaches the x-axis and y-axis, which are the asymptotes of the graph.

STEP 9

The graph is undefined at $x=$ because we cannot divide by zero. This is why there is a gap in the graph at $x=$ .

STEP 10

The graph is symmetric with respect to the origin. This means that if you rotate the graph180 degrees around the origin, you will get the same graph.

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QuestionCreate a table and graph for g(x)=2xg(x)=\frac{2}{x}g(x)=x2​, then describe the graph in detail.

Studdy Solution

STEP 1

Assumptions1. The function is g(x)=xg(x)=\frac{}{x}g(x)=x​ . We need to create a table and a graph for this function3. We need to describe the graph completely

STEP 2

Let's start by creating a table of values for the function g(x)=2xg(x)=\frac{2}{x}g(x)=x2​. We can choose a few values for xxx and calculate the corresponding g(x)g(x)g(x) values.

STEP 3

Choose the values for xxx. Let's choose -3, -2, -1,0,1,2,3.

STEP 4

STEP 5

Now that we have the table of values, we can plot these points on a graph.

STEP 6

Plot the points (-3, -2/3), (-2, -1), (-1, -2), (1,2), (2,1), (3,2/3) on the graph.

STEP 7

Connect the points with a smooth curve to represent the function g(x)=2xg(x)=\frac{2}{x}g(x)=x2​.

STEP 8

The graph of the function g(x)=2xg(x)=\frac{2}{x}g(x)=x2​ is a hyperbola. It has two branches, one in the first quadrant and one in the third quadrant. The graph approaches but never reaches the x-axis and y-axis, which are the asymptotes of the graph.

STEP 9

The graph is undefined at x=x=x= because we cannot divide by zero. This is why there is a gap in the graph at x=x=x=.

STEP 10

The graph is symmetric with respect to the origin. This means that if you rotate the graph180 degrees around the origin, you will get the same graph.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionCreate a table and graph for $g(x)=\frac{2}{x}$ , then describe the graph in detail.

Assumptions1. The function is $g(x)=\frac{}{x}$ . We need to create a table and a graph for this function3. We need to describe the graph completely

Let's start by creating a table of values for the function $g(x)=\frac{2}{x}$ . We can choose a few values for $x$ and calculate the corresponding $g(x)$ values.

Choose the values for $x$ . Let's choose -3, -2, -1,0,1,2,3.

Connect the points with a smooth curve to represent the function $g(x)=\frac{2}{x}$ .

The graph of the function $g(x)=\frac{2}{x}$ is a hyperbola. It has two branches, one in the first quadrant and one in the third quadrant. The graph approaches but never reaches the x-axis and y-axis, which are the asymptotes of the graph.

The graph is undefined at $x=$ because we cannot divide by zero. This is why there is a gap in the graph at $x=$ .