Question

I really don’t understand these Algebra problems, help please. I need to explain/show work.

Answer 1

Step-by-step explanation:

First problem:

The domain is every possible x value that the function can have. For a graph to be a function, there can only be one y value for each x value.

In this case, the graph can have any x value that is between -4 and 2.

This can be written as an interval as such [-4,2] (A=-4, B=3)

The brackets mean that the interval includes the numbers on the end. The filled in black dots on the end of the graph indicate that they are included.

The range is every possible y value that the graph can have. It does not matter how many times the same y value occurs on the graph.

In this case, the y value can be any value between -3 and 3.

This can be written as the interval [-3,3] (C=-3, D=3)

Second problem:

For this problem, the number of quarters will be the domain and the range will be the value of those quarters.

In the domain, we know that there cannot be less than 0 quarters, so that will be one of our limits. We also know that at most, the quarters will be worth $1.50. This means that the maximum number of quarters will be 6. We also know that there cannot be a fraction of a quarter. This means that the number must be an integer, or whole number.

This means that the domain would be: The integers from 0 to 6

For the range, we know that the least amount of $ the quarters could be worth is 0 and the maximum would be $1.50. We also know that this number will increase in intervals of $0.25.

This means that the range would be: {0, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50}

Third problem:

In this problem, we need to know what the graph would look. Like. I've included a picture.

As this graph is a negative parabola, it means that it will be increasing and then decreasing.

As you can see in the graph, the graph changes from increasing to decreasing at x=0.

This means that from -8 to 0 the graph is increasing and from 0 to 8 the graph is decreasing

A= -8, B= 0, C= 0, D= 8

Fourth problem:

As previously stated, for something to be a function, there can only be one value for each x value.

This relation shows only one line from each x value. This means that it IS a function.

This would be as: every element in the domain is mapped to exactly one element in the range.

The final two are correct, but they do not cause the relation to be a function.

I hope this helps. Good Luck!