A function is graft on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach negative infinity. To which family of functions might the describe the function belong?

A: absolute value
B: exponential
C: cube root
D: Square root

C. Cube root

Step-by-step explanation:

Domain is all the possible x-values that the function can have. Range is the possible y-values that the function can have.

When domain approaches infinity, that's just talking about the right of the x-axis and all those values. When domain approaches negative infinity, that's talking about the left of the x-axis. It's the same concept for range.

Here, we know that as domain goes to infinity, range goes to infinity as well, so imagine a graph whose line is going up and right forever. We also know that as domain goes to negative infinity, range goes to negative infinity, too, so imagine the other half of that line going down and left.

This kind of graph is always the characteristic of cube root functions, which are called "odd" functions.

Thus, the answer is C.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

sample answer: you can determine whether each element of the domain is paired with exactly one element of the range. for example, if given a graph, you could use the vertical line test; if a vertical line intersects the graph more than once, then the relation that the graph represents is not a function.