The ordered pairs (1,2),(2,4),(3,8),(4,16), and (5,32) represent a function?
a. y=x^2
b. y=2x
c. y=2^x
d. y=x+2******
The ordered pairs (1,16),(2,25),(3,36),(4,49), and (5,64) represent a function. What is a rule that represents this function?
a. y=x^2
b. y=x+15
c. y=2(x+3)***
d. y=(x+3)^2
first one: y = 2^x
why did you possible pick c)
not a single one of the pairs given satisfies that equation.
It is clearly y = (x+3)^2 , that is, d)
a. y=x^2
Why did the scarecrow win an award?
Because he was outstanding in his field!
For the first question, to determine whether the ordered pairs represent a function, we need to check if each x-value only maps to one y-value.
Let's check the x-values and their corresponding y-values:
For x = 1, y = 2.
For x = 2, y = 4.
For x = 3, y = 8.
For x = 4, y = 16.
For x = 5, y = 32.
As each x-value maps to a unique y-value, this represents a function. Now let's find the rule for this function.
Looking at the y-values, notice that they are the result of squaring the x-values. Therefore, the rule that represents this function is:
a. y = x^2.
For the second question, we need to find a rule that represents the given set of ordered pairs.
Let's check the x-values and their corresponding y-values:
For x = 1, y = 16.
For x = 2, y = 25.
For x = 3, y = 36.
For x = 4, y = 49.
For x = 5, y = 64.
To find the rule, let's check how the y-values change in relation to the x-values. Notice that the y-values are always 15 more than the square of the x-values. Therefore, the rule that represents this function is:
b. y = x^2 + 15.
To determine if a set of ordered pairs represents a function, we need to check if each x-value is associated with a unique y-value. In other words, there shouldn't be two different ordered pairs with the same x-value but different y-values.
For the first set of ordered pairs: (1,2),(2,4),(3,8),(4,16), and (5,32)
We can observe that each x-value has a unique y-value. Moreover, if we try to represent these values using equations, we can see that the y-values are increasing exponentially as the x-values increase.
To find the equation for this function, we can observe that the y-values seem to be doubling as the x-values increase. We can write this as y = 2^x (c) which represents exponential growth.
Therefore, the answer to the first question is c. y=2^x.
Now, for the second set of ordered pairs: (1,16),(2,25),(3,36),(4,49), and (5,64)
Again, each x-value has a unique y-value. By observing the y-values, we can see that they are the perfect squares of the corresponding x-values.
To find the equation for this function, we can write y = x^2 (a) as it represents the relationship between x and y where y is the square of x.
Therefore, the answer to the second question is a. y=x^2.