PLEASE ANSWER!!! Select the correct answer from each drop-down menu. Consider the function f(x) = 3x + 1 and the graph of the fu
nction g(x) shown below.
2 answers:
Answer:
Translation of 2 units to the right
g(x) = f(x-2)
Step-by-step explanation:
Given the original function f (x) = 3x +1, we can get the function plotted by translating the graph 2 units to the right.
As seen in the attached image, the original function f(x) is shown in orange, while the translation 2 units to the right is the function in blue. Notice that in the original function the crossing of the x-axis occurs at x = -1/3, and translating the function to the right 2 units moves the crossing two full units to the right, making it now cross the x-axis at x = 5/3
Such translation in 2 units to the right corresponds to a subtraction of 2 units from the x-variable in the original functional expression:
g (x) = f (x - 2) g (x) = 3(x - 2) + 1
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Answer:
The numbers are 12 and 3.
Step-by-step explanation:
We can solve this problem by working with the information we have and setting up some equations.
We know that one number is four times as large as another. So, let the smaller number be represented by the variable x and the bigger number be represented by 4x, since it is four times as large.
Now, we know that if the numbers are added together, then the result is six less than seven times the smaller number. This can also be represented by the equation 4x + x = 7x - 6.
Let's solve that equation like so:
So, the smaller number must be 3 (remember that x represented the smaller number). To find the bigger number, all we need to do is multiply 3 by 4, which gives us 12. Therefore, the numbers are 12 and 3.