A "vertical" line is defined by the equation x = a, where a is any real number. A relation represented by x = a is not a function. This is because for a relation to be a function, each input (x value) must correspond to exactly one output (y value). In the case of x = a, any y value can correspond to the single x value of a, so it is not a function.

If we graph y = a, the graph will be a "horizontal" line. A relation represented by y = a is a function. This is because for each input (x value), there is exactly one output (y value), which is a.

Now, let's determine which of the following relations are functions:

1. 𝑦 = 5: This is a function. No matter what x value you input, you will always get a single output of 5.

2. 𝑦 = 2𝑥 − 5: This is a function. For each x value, there is exactly one y value determined by the equation 2x - 5.

3. 𝑥 = −2: This is not a function. As explained above, any equation of the form x = a is not a function because any y value can correspond to the single x value of a.

4. 2𝑦 = 𝑥 − 4: This is a function. If we rearrange this equation to solve for y, we get y = (x - 4) / 2. For each x value, there is exactly one y value determined by this equation.

Question

A "vertical" line is defined by the equation x = a, where a is any real number. A relation represented by x = a is not a function. This is because for a relation to be a function, each input (x value) must correspond to exactly one output (y value). In the case of x = a, any y value can correspond to the single x value of a, so it is not a function.

If we graph y = a, the graph will be a "horizontal" line. A relation represented by y = a is a function. This is because for each input (x value), there is exactly one output (y value), which is a.

Now, let's determine which of the following relations are functions:

1. 𝑦 = 5: This is a function. No matter what x value you input, you will always get a single output of 5.

2. 𝑦 = 2𝑥 − 5: This is a function. For each x value, there is exactly one y value determined by the equation 2x - 5.

3. 𝑥 = −2: This is not a function. As explained above, any equation of the form x = a is not a function because any y value can correspond to the single x value of a.

4. 2𝑦 = 𝑥 − 4: This is a function. If we rearrange this equation to solve for y, we get y = (x - 4) / 2. For each x value, there is exactly one y value determined by this equation.

Knowee AI · Accepted Answer

A "vertical" line is defined by the equation x = a, where a is any real number. A relation represented by x = a is not a function. This is because for a relation to be a function, each input (x value) must correspond to exactly one output (y value). In the case of x = a, any y value can correspond to the single x value of a, so it is not a function.

If we graph y = a, the graph will be a "horizontal" line. A relation represented by y = a is a function. This is because for each input (x value), there is exactly one output (y value), which is a.

Now, let's determine which of the following relations are functions:

1. 𝑦 = 5: This is a function. No matter what x value you input, you will always get a single output of 5.

2. 𝑦 = 2𝑥 − 5: This is a function. For each x value, there is exactly one y value determined by the equation 2x - 5.

3. 𝑥 = −2: This is not a function. As explained above, any equation of the form x = a is not a function because any y value can correspond to the single x value of a.

4. 2𝑦 = 𝑥 − 4: This is a function. If we rearrange this equation to solve for y, we get y = (x - 4) / 2. For each x value, there is exactly one y value determined by this equation.

Question

Solution

Similar Questions

Upgrade your grade with Knowee