Suppose the graph of a polynomial function P(x) has an x-intercept at (c,0) . Write 4-6 sentences analyzing whether (c,0) is also an x-intercept of the graphs that result from applying single transformations to P(x) . For each transformation, elaborate on whether (c,0) is always, sometimes, or never an x-intercept of the transformed graph, explaining your reasoning. For any transformations for which (c,0) is only sometimes an x-intercept of the transformed graph, design specific functions to illustrate how the other x-intercepts of the original graph determine whether (c,0) is an x-intercept of the transformed graph.

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.

probably the last option

step-by-step explanation:

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.