Which transformations have been performed on the graph of f(x) = to obtain the graph g(x) = 1/4 + 6 select each correct answer. (a) reflect the graph over the x-axis (b) compress the graph closer to the x-axis (c) translate the graph down (d) translate the graph to the right (e) translate the graph to the left (f) translate the graph up (g) stretch the graph away from the x-axis

The correct answers are B, E and F

Step-by-step explanation:

We can find the answer B by noticing the 1/4 put in front of the cube root sign. this 1/4 shirks the value of every y value by 1/4, which in turn makes it closer to the x axis.

We can find answer E by looking at the 3 inside of the cube root symbol. When we add a number underneath the cube root sign, it always moves the value to the left that many spaces.

Finally, we can find F by looking at the 6 at the end. Any number added to the end of an equation as a constant moves the graph up by that many spaces.

in mathematics, a function is a relationship between two variables such that the value of one of the variables, called the dependent variable, is determined by the value of the other variable, called the independent variable. there is a specific term we use to describe the set of independent variables of a function.

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range: